[
  {
    "id": "outcome-facts-four-bit-0-mean-outside-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/2; value 8 with probability 1/2. Sum masses for equal values. The candidate x is 5 units. Independently computed facts supplied for this question: exact weighted mean = 5; full set of modes = 2, 8; full support = 2, 8; probability of candidate x = 0. Statement: Under FI-0-mean-outside, the probability-weighted mean is 5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/2; value 8 with probability 1/2. Sum masses for equal values. The candidate x is 5 units. Independently computed facts supplied for this question: exact weighted mean = 5; full set of modes = 2, 8; full support = 2, 8; probability of candidate x = 0. Statement: 5 units is mean-outcome(FI-0-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "toy output",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mean-outside-mean-outcome-True",
    "oracle": {
      "mean": "5",
      "modes": [
        "2",
        "8"
      ],
      "x": "5",
      "masses": {
        "2": "1/2",
        "8": "1/2"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-mean-outside-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/2; value 8 with probability 1/2. Sum masses for equal values. The candidate x is 6 units. Independently computed facts supplied for this question: exact weighted mean = 5; full set of modes = 2, 8; full support = 2, 8; probability of candidate x = 0. Statement: Under FI-0-mean-outside, the probability-weighted mean is 6 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/2; value 8 with probability 1/2. Sum masses for equal values. The candidate x is 6 units. Independently computed facts supplied for this question: exact weighted mean = 5; full set of modes = 2, 8; full support = 2, 8; probability of candidate x = 0. Statement: 6 units is mean-outcome(FI-0-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "toy output",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mean-outside-mean-outcome-False",
    "oracle": {
      "mean": "5",
      "modes": [
        "2",
        "8"
      ],
      "x": "6",
      "masses": {
        "2": "1/2",
        "8": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-mean-outside-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/2; value 8 with probability 1/2. Sum masses for equal values. The candidate x is 2 units. Independently computed facts supplied for this question: exact weighted mean = 5; full set of modes = 2, 8; full support = 2, 8; probability of candidate x = 1/2. Statement: Under FI-0-mean-outside, 2 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/2; value 8 with probability 1/2. Sum masses for equal values. The candidate x is 2 units. Independently computed facts supplied for this question: exact weighted mean = 5; full set of modes = 2, 8; full support = 2, 8; probability of candidate x = 1/2. Statement: 2 units is likeliest-outcome(FI-0-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "toy output",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mean-outside-likeliest-outcome-True",
    "oracle": {
      "mean": "5",
      "modes": [
        "2",
        "8"
      ],
      "x": "2",
      "masses": {
        "2": "1/2",
        "8": "1/2"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-mean-outside-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/2; value 8 with probability 1/2. Sum masses for equal values. The candidate x is 1 units. Independently computed facts supplied for this question: exact weighted mean = 5; full set of modes = 2, 8; full support = 2, 8; probability of candidate x = 0. Statement: Under FI-0-mean-outside, 1 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/2; value 8 with probability 1/2. Sum masses for equal values. The candidate x is 1 units. Independently computed facts supplied for this question: exact weighted mean = 5; full set of modes = 2, 8; full support = 2, 8; probability of candidate x = 0. Statement: 1 units is likeliest-outcome(FI-0-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "toy output",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mean-outside-likeliest-outcome-False",
    "oracle": {
      "mean": "5",
      "modes": [
        "2",
        "8"
      ],
      "x": "1",
      "masses": {
        "2": "1/2",
        "8": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-mode-below-half-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 6 with probability 3/10; value 12 with probability 3/10. Sum masses for equal values. The candidate x is 31/5 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2; full support = 2, 6, 12; probability of candidate x = 0. Statement: Under FI-0-mode-below-half, the probability-weighted mean is 31/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 6 with probability 3/10; value 12 with probability 3/10. Sum masses for equal values. The candidate x is 31/5 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2; full support = 2, 6, 12; probability of candidate x = 0. Statement: 31/5 units is mean-outcome(FI-0-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "toy output",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mode-below-half-mean-outcome-True",
    "oracle": {
      "mean": "31/5",
      "modes": [
        "2"
      ],
      "x": "31/5",
      "masses": {
        "2": "2/5",
        "6": "3/10",
        "12": "3/10"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-mode-below-half-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 6 with probability 3/10; value 12 with probability 3/10. Sum masses for equal values. The candidate x is 36/5 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2; full support = 2, 6, 12; probability of candidate x = 0. Statement: Under FI-0-mode-below-half, the probability-weighted mean is 36/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 6 with probability 3/10; value 12 with probability 3/10. Sum masses for equal values. The candidate x is 36/5 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2; full support = 2, 6, 12; probability of candidate x = 0. Statement: 36/5 units is mean-outcome(FI-0-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "toy output",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mode-below-half-mean-outcome-False",
    "oracle": {
      "mean": "31/5",
      "modes": [
        "2"
      ],
      "x": "36/5",
      "masses": {
        "2": "2/5",
        "6": "3/10",
        "12": "3/10"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-mode-below-half-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 6 with probability 3/10; value 12 with probability 3/10. Sum masses for equal values. The candidate x is 2 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2; full support = 2, 6, 12; probability of candidate x = 2/5. Statement: Under FI-0-mode-below-half, 2 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 6 with probability 3/10; value 12 with probability 3/10. Sum masses for equal values. The candidate x is 2 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2; full support = 2, 6, 12; probability of candidate x = 2/5. Statement: 2 units is likeliest-outcome(FI-0-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "toy output",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mode-below-half-likeliest-outcome-True",
    "oracle": {
      "mean": "31/5",
      "modes": [
        "2"
      ],
      "x": "2",
      "masses": {
        "2": "2/5",
        "6": "3/10",
        "12": "3/10"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-mode-below-half-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 6 with probability 3/10; value 12 with probability 3/10. Sum masses for equal values. The candidate x is 1 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2; full support = 2, 6, 12; probability of candidate x = 0. Statement: Under FI-0-mode-below-half, 1 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 6 with probability 3/10; value 12 with probability 3/10. Sum masses for equal values. The candidate x is 1 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2; full support = 2, 6, 12; probability of candidate x = 0. Statement: 1 units is likeliest-outcome(FI-0-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "toy output",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mode-below-half-likeliest-outcome-False",
    "oracle": {
      "mean": "31/5",
      "modes": [
        "2"
      ],
      "x": "1",
      "masses": {
        "2": "2/5",
        "6": "3/10",
        "12": "3/10"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-tied-modes-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 8 with probability 2/5; value 11 with probability 1/5. Sum masses for equal values. The candidate x is 31/5 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2, 8; full support = 2, 8, 11; probability of candidate x = 0. Statement: Under FI-0-tied-modes, the probability-weighted mean is 31/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 8 with probability 2/5; value 11 with probability 1/5. Sum masses for equal values. The candidate x is 31/5 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2, 8; full support = 2, 8, 11; probability of candidate x = 0. Statement: 31/5 units is mean-outcome(FI-0-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "toy output",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-tied-modes-mean-outcome-True",
    "oracle": {
      "mean": "31/5",
      "modes": [
        "2",
        "8"
      ],
      "x": "31/5",
      "masses": {
        "2": "2/5",
        "8": "2/5",
        "11": "1/5"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-tied-modes-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 8 with probability 2/5; value 11 with probability 1/5. Sum masses for equal values. The candidate x is 36/5 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2, 8; full support = 2, 8, 11; probability of candidate x = 0. Statement: Under FI-0-tied-modes, the probability-weighted mean is 36/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 8 with probability 2/5; value 11 with probability 1/5. Sum masses for equal values. The candidate x is 36/5 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2, 8; full support = 2, 8, 11; probability of candidate x = 0. Statement: 36/5 units is mean-outcome(FI-0-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "toy output",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-tied-modes-mean-outcome-False",
    "oracle": {
      "mean": "31/5",
      "modes": [
        "2",
        "8"
      ],
      "x": "36/5",
      "masses": {
        "2": "2/5",
        "8": "2/5",
        "11": "1/5"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-tied-modes-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 8 with probability 2/5; value 11 with probability 1/5. Sum masses for equal values. The candidate x is 2 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2, 8; full support = 2, 8, 11; probability of candidate x = 2/5. Statement: Under FI-0-tied-modes, 2 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 8 with probability 2/5; value 11 with probability 1/5. Sum masses for equal values. The candidate x is 2 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2, 8; full support = 2, 8, 11; probability of candidate x = 2/5. Statement: 2 units is likeliest-outcome(FI-0-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "toy output",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-tied-modes-likeliest-outcome-True",
    "oracle": {
      "mean": "31/5",
      "modes": [
        "2",
        "8"
      ],
      "x": "2",
      "masses": {
        "2": "2/5",
        "8": "2/5",
        "11": "1/5"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-tied-modes-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 8 with probability 2/5; value 11 with probability 1/5. Sum masses for equal values. The candidate x is 1 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2, 8; full support = 2, 8, 11; probability of candidate x = 0. Statement: Under FI-0-tied-modes, 1 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 2/5; value 8 with probability 2/5; value 11 with probability 1/5. Sum masses for equal values. The candidate x is 1 units. Independently computed facts supplied for this question: exact weighted mean = 31/5; full set of modes = 2, 8; full support = 2, 8, 11; probability of candidate x = 0. Statement: 1 units is likeliest-outcome(FI-0-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "toy output",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-tied-modes-likeliest-outcome-False",
    "oracle": {
      "mean": "31/5",
      "modes": [
        "2",
        "8"
      ],
      "x": "1",
      "masses": {
        "2": "2/5",
        "8": "2/5",
        "11": "1/5"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-mean-is-mode-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/4; value 6 with probability 1/2; value 10 with probability 1/4. Sum masses for equal values. The candidate x is 6 units. Independently computed facts supplied for this question: exact weighted mean = 6; full set of modes = 6; full support = 2, 6, 10; probability of candidate x = 1/2. Statement: Under FI-0-mean-is-mode, the probability-weighted mean is 6 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/4; value 6 with probability 1/2; value 10 with probability 1/4. Sum masses for equal values. The candidate x is 6 units. Independently computed facts supplied for this question: exact weighted mean = 6; full set of modes = 6; full support = 2, 6, 10; probability of candidate x = 1/2. Statement: 6 units is mean-outcome(FI-0-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "toy output",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mean-is-mode-mean-outcome-True",
    "oracle": {
      "mean": "6",
      "modes": [
        "6"
      ],
      "x": "6",
      "masses": {
        "2": "1/4",
        "6": "1/2",
        "10": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-mean-is-mode-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/4; value 6 with probability 1/2; value 10 with probability 1/4. Sum masses for equal values. The candidate x is 7 units. Independently computed facts supplied for this question: exact weighted mean = 6; full set of modes = 6; full support = 2, 6, 10; probability of candidate x = 0. Statement: Under FI-0-mean-is-mode, the probability-weighted mean is 7 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/4; value 6 with probability 1/2; value 10 with probability 1/4. Sum masses for equal values. The candidate x is 7 units. Independently computed facts supplied for this question: exact weighted mean = 6; full set of modes = 6; full support = 2, 6, 10; probability of candidate x = 0. Statement: 7 units is mean-outcome(FI-0-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "toy output",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mean-is-mode-mean-outcome-False",
    "oracle": {
      "mean": "6",
      "modes": [
        "6"
      ],
      "x": "7",
      "masses": {
        "2": "1/4",
        "6": "1/2",
        "10": "1/4"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-mean-is-mode-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/4; value 6 with probability 1/2; value 10 with probability 1/4. Sum masses for equal values. The candidate x is 6 units. Independently computed facts supplied for this question: exact weighted mean = 6; full set of modes = 6; full support = 2, 6, 10; probability of candidate x = 1/2. Statement: Under FI-0-mean-is-mode, 6 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/4; value 6 with probability 1/2; value 10 with probability 1/4. Sum masses for equal values. The candidate x is 6 units. Independently computed facts supplied for this question: exact weighted mean = 6; full set of modes = 6; full support = 2, 6, 10; probability of candidate x = 1/2. Statement: 6 units is likeliest-outcome(FI-0-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "toy output",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mean-is-mode-likeliest-outcome-True",
    "oracle": {
      "mean": "6",
      "modes": [
        "6"
      ],
      "x": "6",
      "masses": {
        "2": "1/4",
        "6": "1/2",
        "10": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-mean-is-mode-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/4; value 6 with probability 1/2; value 10 with probability 1/4. Sum masses for equal values. The candidate x is 1 units. Independently computed facts supplied for this question: exact weighted mean = 6; full set of modes = 6; full support = 2, 6, 10; probability of candidate x = 0. Statement: Under FI-0-mean-is-mode, 1 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 2 with probability 1/4; value 6 with probability 1/2; value 10 with probability 1/4. Sum masses for equal values. The candidate x is 1 units. Independently computed facts supplied for this question: exact weighted mean = 6; full set of modes = 6; full support = 2, 6, 10; probability of candidate x = 0. Statement: 1 units is likeliest-outcome(FI-0-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "toy output",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-mean-is-mode-likeliest-outcome-False",
    "oracle": {
      "mean": "6",
      "modes": [
        "6"
      ],
      "x": "1",
      "masses": {
        "2": "1/4",
        "6": "1/2",
        "10": "1/4"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-duplicate-paths-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 3 with probability 1/4; value 3 with probability 1/4; value 9 with probability 1/3; value 12 with probability 1/6. Sum masses for equal values. The candidate x is 13/2 units. Independently computed facts supplied for this question: exact weighted mean = 13/2; full set of modes = 3; full support = 3, 9, 12; probability of candidate x = 0. Statement: Under FI-0-duplicate-paths, the probability-weighted mean is 13/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 3 with probability 1/4; value 3 with probability 1/4; value 9 with probability 1/3; value 12 with probability 1/6. Sum masses for equal values. The candidate x is 13/2 units. Independently computed facts supplied for this question: exact weighted mean = 13/2; full set of modes = 3; full support = 3, 9, 12; probability of candidate x = 0. Statement: 13/2 units is mean-outcome(FI-0-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "toy output",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-duplicate-paths-mean-outcome-True",
    "oracle": {
      "mean": "13/2",
      "modes": [
        "3"
      ],
      "x": "13/2",
      "masses": {
        "3": "1/2",
        "9": "1/3",
        "12": "1/6"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-duplicate-paths-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 3 with probability 1/4; value 3 with probability 1/4; value 9 with probability 1/3; value 12 with probability 1/6. Sum masses for equal values. The candidate x is 15/2 units. Independently computed facts supplied for this question: exact weighted mean = 13/2; full set of modes = 3; full support = 3, 9, 12; probability of candidate x = 0. Statement: Under FI-0-duplicate-paths, the probability-weighted mean is 15/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 3 with probability 1/4; value 3 with probability 1/4; value 9 with probability 1/3; value 12 with probability 1/6. Sum masses for equal values. The candidate x is 15/2 units. Independently computed facts supplied for this question: exact weighted mean = 13/2; full set of modes = 3; full support = 3, 9, 12; probability of candidate x = 0. Statement: 15/2 units is mean-outcome(FI-0-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "toy output",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-duplicate-paths-mean-outcome-False",
    "oracle": {
      "mean": "13/2",
      "modes": [
        "3"
      ],
      "x": "15/2",
      "masses": {
        "3": "1/2",
        "9": "1/3",
        "12": "1/6"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-duplicate-paths-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 3 with probability 1/4; value 3 with probability 1/4; value 9 with probability 1/3; value 12 with probability 1/6. Sum masses for equal values. The candidate x is 3 units. Independently computed facts supplied for this question: exact weighted mean = 13/2; full set of modes = 3; full support = 3, 9, 12; probability of candidate x = 1/2. Statement: Under FI-0-duplicate-paths, 3 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 3 with probability 1/4; value 3 with probability 1/4; value 9 with probability 1/3; value 12 with probability 1/6. Sum masses for equal values. The candidate x is 3 units. Independently computed facts supplied for this question: exact weighted mean = 13/2; full set of modes = 3; full support = 3, 9, 12; probability of candidate x = 1/2. Statement: 3 units is likeliest-outcome(FI-0-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "toy output",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-duplicate-paths-likeliest-outcome-True",
    "oracle": {
      "mean": "13/2",
      "modes": [
        "3"
      ],
      "x": "3",
      "masses": {
        "3": "1/2",
        "9": "1/3",
        "12": "1/6"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-0-duplicate-paths-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 3 with probability 1/4; value 3 with probability 1/4; value 9 with probability 1/3; value 12 with probability 1/6. Sum masses for equal values. The candidate x is 2 units. Independently computed facts supplied for this question: exact weighted mean = 13/2; full set of modes = 3; full support = 3, 9, 12; probability of candidate x = 0. Statement: Under FI-0-duplicate-paths, 2 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional toy output model FI-0-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 3 with probability 1/4; value 3 with probability 1/4; value 9 with probability 1/3; value 12 with probability 1/6. Sum masses for equal values. The candidate x is 2 units. Independently computed facts supplied for this question: exact weighted mean = 13/2; full set of modes = 3; full support = 3, 9, 12; probability of candidate x = 0. Statement: 2 units is likeliest-outcome(FI-0-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "toy output",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "0-duplicate-paths-likeliest-outcome-False",
    "oracle": {
      "mean": "13/2",
      "modes": [
        "3"
      ],
      "x": "2",
      "masses": {
        "3": "1/2",
        "9": "1/3",
        "12": "1/6"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mean-outside-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/2; value 21 with probability 1/2. Sum masses for equal values. The candidate x is 18 units. Independently computed facts supplied for this question: exact weighted mean = 18; full set of modes = 15, 21; full support = 15, 21; probability of candidate x = 0. Statement: Under FI-1-mean-outside, the probability-weighted mean is 18 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/2; value 21 with probability 1/2. Sum masses for equal values. The candidate x is 18 units. Independently computed facts supplied for this question: exact weighted mean = 18; full set of modes = 15, 21; full support = 15, 21; probability of candidate x = 0. Statement: 18 units is mean-outcome(FI-1-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "queue delay",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mean-outside-mean-outcome-True",
    "oracle": {
      "mean": "18",
      "modes": [
        "15",
        "21"
      ],
      "x": "18",
      "masses": {
        "15": "1/2",
        "21": "1/2"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mean-outside-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/2; value 21 with probability 1/2. Sum masses for equal values. The candidate x is 19 units. Independently computed facts supplied for this question: exact weighted mean = 18; full set of modes = 15, 21; full support = 15, 21; probability of candidate x = 0. Statement: Under FI-1-mean-outside, the probability-weighted mean is 19 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/2; value 21 with probability 1/2. Sum masses for equal values. The candidate x is 19 units. Independently computed facts supplied for this question: exact weighted mean = 18; full set of modes = 15, 21; full support = 15, 21; probability of candidate x = 0. Statement: 19 units is mean-outcome(FI-1-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "queue delay",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mean-outside-mean-outcome-False",
    "oracle": {
      "mean": "18",
      "modes": [
        "15",
        "21"
      ],
      "x": "19",
      "masses": {
        "15": "1/2",
        "21": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mean-outside-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/2; value 21 with probability 1/2. Sum masses for equal values. The candidate x is 21 units. Independently computed facts supplied for this question: exact weighted mean = 18; full set of modes = 15, 21; full support = 15, 21; probability of candidate x = 1/2. Statement: Under FI-1-mean-outside, 21 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/2; value 21 with probability 1/2. Sum masses for equal values. The candidate x is 21 units. Independently computed facts supplied for this question: exact weighted mean = 18; full set of modes = 15, 21; full support = 15, 21; probability of candidate x = 1/2. Statement: 21 units is likeliest-outcome(FI-1-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "queue delay",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mean-outside-likeliest-outcome-True",
    "oracle": {
      "mean": "18",
      "modes": [
        "15",
        "21"
      ],
      "x": "21",
      "masses": {
        "15": "1/2",
        "21": "1/2"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mean-outside-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/2; value 21 with probability 1/2. Sum masses for equal values. The candidate x is 14 units. Independently computed facts supplied for this question: exact weighted mean = 18; full set of modes = 15, 21; full support = 15, 21; probability of candidate x = 0. Statement: Under FI-1-mean-outside, 14 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/2; value 21 with probability 1/2. Sum masses for equal values. The candidate x is 14 units. Independently computed facts supplied for this question: exact weighted mean = 18; full set of modes = 15, 21; full support = 15, 21; probability of candidate x = 0. Statement: 14 units is likeliest-outcome(FI-1-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "queue delay",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mean-outside-likeliest-outcome-False",
    "oracle": {
      "mean": "18",
      "modes": [
        "15",
        "21"
      ],
      "x": "14",
      "masses": {
        "15": "1/2",
        "21": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mode-below-half-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 19 with probability 3/10; value 25 with probability 3/10. Sum masses for equal values. The candidate x is 96/5 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15; full support = 15, 19, 25; probability of candidate x = 0. Statement: Under FI-1-mode-below-half, the probability-weighted mean is 96/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 19 with probability 3/10; value 25 with probability 3/10. Sum masses for equal values. The candidate x is 96/5 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15; full support = 15, 19, 25; probability of candidate x = 0. Statement: 96/5 units is mean-outcome(FI-1-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "queue delay",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mode-below-half-mean-outcome-True",
    "oracle": {
      "mean": "96/5",
      "modes": [
        "15"
      ],
      "x": "96/5",
      "masses": {
        "15": "2/5",
        "19": "3/10",
        "25": "3/10"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mode-below-half-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 19 with probability 3/10; value 25 with probability 3/10. Sum masses for equal values. The candidate x is 101/5 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15; full support = 15, 19, 25; probability of candidate x = 0. Statement: Under FI-1-mode-below-half, the probability-weighted mean is 101/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 19 with probability 3/10; value 25 with probability 3/10. Sum masses for equal values. The candidate x is 101/5 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15; full support = 15, 19, 25; probability of candidate x = 0. Statement: 101/5 units is mean-outcome(FI-1-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "queue delay",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mode-below-half-mean-outcome-False",
    "oracle": {
      "mean": "96/5",
      "modes": [
        "15"
      ],
      "x": "101/5",
      "masses": {
        "15": "2/5",
        "19": "3/10",
        "25": "3/10"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mode-below-half-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 19 with probability 3/10; value 25 with probability 3/10. Sum masses for equal values. The candidate x is 15 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15; full support = 15, 19, 25; probability of candidate x = 2/5. Statement: Under FI-1-mode-below-half, 15 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 19 with probability 3/10; value 25 with probability 3/10. Sum masses for equal values. The candidate x is 15 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15; full support = 15, 19, 25; probability of candidate x = 2/5. Statement: 15 units is likeliest-outcome(FI-1-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "queue delay",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mode-below-half-likeliest-outcome-True",
    "oracle": {
      "mean": "96/5",
      "modes": [
        "15"
      ],
      "x": "15",
      "masses": {
        "15": "2/5",
        "19": "3/10",
        "25": "3/10"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mode-below-half-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 19 with probability 3/10; value 25 with probability 3/10. Sum masses for equal values. The candidate x is 19 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15; full support = 15, 19, 25; probability of candidate x = 3/10. Statement: Under FI-1-mode-below-half, 19 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 19 with probability 3/10; value 25 with probability 3/10. Sum masses for equal values. The candidate x is 19 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15; full support = 15, 19, 25; probability of candidate x = 3/10. Statement: 19 units is likeliest-outcome(FI-1-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "queue delay",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mode-below-half-likeliest-outcome-False",
    "oracle": {
      "mean": "96/5",
      "modes": [
        "15"
      ],
      "x": "19",
      "masses": {
        "15": "2/5",
        "19": "3/10",
        "25": "3/10"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-tied-modes-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 21 with probability 2/5; value 24 with probability 1/5. Sum masses for equal values. The candidate x is 96/5 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15, 21; full support = 15, 21, 24; probability of candidate x = 0. Statement: Under FI-1-tied-modes, the probability-weighted mean is 96/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 21 with probability 2/5; value 24 with probability 1/5. Sum masses for equal values. The candidate x is 96/5 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15, 21; full support = 15, 21, 24; probability of candidate x = 0. Statement: 96/5 units is mean-outcome(FI-1-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "queue delay",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-tied-modes-mean-outcome-True",
    "oracle": {
      "mean": "96/5",
      "modes": [
        "15",
        "21"
      ],
      "x": "96/5",
      "masses": {
        "15": "2/5",
        "21": "2/5",
        "24": "1/5"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-tied-modes-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 21 with probability 2/5; value 24 with probability 1/5. Sum masses for equal values. The candidate x is 101/5 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15, 21; full support = 15, 21, 24; probability of candidate x = 0. Statement: Under FI-1-tied-modes, the probability-weighted mean is 101/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 21 with probability 2/5; value 24 with probability 1/5. Sum masses for equal values. The candidate x is 101/5 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15, 21; full support = 15, 21, 24; probability of candidate x = 0. Statement: 101/5 units is mean-outcome(FI-1-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "queue delay",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-tied-modes-mean-outcome-False",
    "oracle": {
      "mean": "96/5",
      "modes": [
        "15",
        "21"
      ],
      "x": "101/5",
      "masses": {
        "15": "2/5",
        "21": "2/5",
        "24": "1/5"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-tied-modes-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 21 with probability 2/5; value 24 with probability 1/5. Sum masses for equal values. The candidate x is 21 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15, 21; full support = 15, 21, 24; probability of candidate x = 2/5. Statement: Under FI-1-tied-modes, 21 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 21 with probability 2/5; value 24 with probability 1/5. Sum masses for equal values. The candidate x is 21 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15, 21; full support = 15, 21, 24; probability of candidate x = 2/5. Statement: 21 units is likeliest-outcome(FI-1-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "queue delay",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-tied-modes-likeliest-outcome-True",
    "oracle": {
      "mean": "96/5",
      "modes": [
        "15",
        "21"
      ],
      "x": "21",
      "masses": {
        "15": "2/5",
        "21": "2/5",
        "24": "1/5"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-tied-modes-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 21 with probability 2/5; value 24 with probability 1/5. Sum masses for equal values. The candidate x is 24 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15, 21; full support = 15, 21, 24; probability of candidate x = 1/5. Statement: Under FI-1-tied-modes, 24 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 2/5; value 21 with probability 2/5; value 24 with probability 1/5. Sum masses for equal values. The candidate x is 24 units. Independently computed facts supplied for this question: exact weighted mean = 96/5; full set of modes = 15, 21; full support = 15, 21, 24; probability of candidate x = 1/5. Statement: 24 units is likeliest-outcome(FI-1-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "queue delay",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-tied-modes-likeliest-outcome-False",
    "oracle": {
      "mean": "96/5",
      "modes": [
        "15",
        "21"
      ],
      "x": "24",
      "masses": {
        "15": "2/5",
        "21": "2/5",
        "24": "1/5"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mean-is-mode-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/4; value 19 with probability 1/2; value 23 with probability 1/4. Sum masses for equal values. The candidate x is 19 units. Independently computed facts supplied for this question: exact weighted mean = 19; full set of modes = 19; full support = 15, 19, 23; probability of candidate x = 1/2. Statement: Under FI-1-mean-is-mode, the probability-weighted mean is 19 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/4; value 19 with probability 1/2; value 23 with probability 1/4. Sum masses for equal values. The candidate x is 19 units. Independently computed facts supplied for this question: exact weighted mean = 19; full set of modes = 19; full support = 15, 19, 23; probability of candidate x = 1/2. Statement: 19 units is mean-outcome(FI-1-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "queue delay",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mean-is-mode-mean-outcome-True",
    "oracle": {
      "mean": "19",
      "modes": [
        "19"
      ],
      "x": "19",
      "masses": {
        "15": "1/4",
        "19": "1/2",
        "23": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mean-is-mode-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/4; value 19 with probability 1/2; value 23 with probability 1/4. Sum masses for equal values. The candidate x is 20 units. Independently computed facts supplied for this question: exact weighted mean = 19; full set of modes = 19; full support = 15, 19, 23; probability of candidate x = 0. Statement: Under FI-1-mean-is-mode, the probability-weighted mean is 20 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/4; value 19 with probability 1/2; value 23 with probability 1/4. Sum masses for equal values. The candidate x is 20 units. Independently computed facts supplied for this question: exact weighted mean = 19; full set of modes = 19; full support = 15, 19, 23; probability of candidate x = 0. Statement: 20 units is mean-outcome(FI-1-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "queue delay",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mean-is-mode-mean-outcome-False",
    "oracle": {
      "mean": "19",
      "modes": [
        "19"
      ],
      "x": "20",
      "masses": {
        "15": "1/4",
        "19": "1/2",
        "23": "1/4"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mean-is-mode-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/4; value 19 with probability 1/2; value 23 with probability 1/4. Sum masses for equal values. The candidate x is 19 units. Independently computed facts supplied for this question: exact weighted mean = 19; full set of modes = 19; full support = 15, 19, 23; probability of candidate x = 1/2. Statement: Under FI-1-mean-is-mode, 19 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/4; value 19 with probability 1/2; value 23 with probability 1/4. Sum masses for equal values. The candidate x is 19 units. Independently computed facts supplied for this question: exact weighted mean = 19; full set of modes = 19; full support = 15, 19, 23; probability of candidate x = 1/2. Statement: 19 units is likeliest-outcome(FI-1-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "queue delay",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mean-is-mode-likeliest-outcome-True",
    "oracle": {
      "mean": "19",
      "modes": [
        "19"
      ],
      "x": "19",
      "masses": {
        "15": "1/4",
        "19": "1/2",
        "23": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-mean-is-mode-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/4; value 19 with probability 1/2; value 23 with probability 1/4. Sum masses for equal values. The candidate x is 15 units. Independently computed facts supplied for this question: exact weighted mean = 19; full set of modes = 19; full support = 15, 19, 23; probability of candidate x = 1/4. Statement: Under FI-1-mean-is-mode, 15 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 15 with probability 1/4; value 19 with probability 1/2; value 23 with probability 1/4. Sum masses for equal values. The candidate x is 15 units. Independently computed facts supplied for this question: exact weighted mean = 19; full set of modes = 19; full support = 15, 19, 23; probability of candidate x = 1/4. Statement: 15 units is likeliest-outcome(FI-1-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "queue delay",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-mean-is-mode-likeliest-outcome-False",
    "oracle": {
      "mean": "19",
      "modes": [
        "19"
      ],
      "x": "15",
      "masses": {
        "15": "1/4",
        "19": "1/2",
        "23": "1/4"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-duplicate-paths-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 16 with probability 1/4; value 16 with probability 1/4; value 22 with probability 1/3; value 25 with probability 1/6. Sum masses for equal values. The candidate x is 39/2 units. Independently computed facts supplied for this question: exact weighted mean = 39/2; full set of modes = 16; full support = 16, 22, 25; probability of candidate x = 0. Statement: Under FI-1-duplicate-paths, the probability-weighted mean is 39/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 16 with probability 1/4; value 16 with probability 1/4; value 22 with probability 1/3; value 25 with probability 1/6. Sum masses for equal values. The candidate x is 39/2 units. Independently computed facts supplied for this question: exact weighted mean = 39/2; full set of modes = 16; full support = 16, 22, 25; probability of candidate x = 0. Statement: 39/2 units is mean-outcome(FI-1-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "queue delay",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-duplicate-paths-mean-outcome-True",
    "oracle": {
      "mean": "39/2",
      "modes": [
        "16"
      ],
      "x": "39/2",
      "masses": {
        "16": "1/2",
        "22": "1/3",
        "25": "1/6"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-duplicate-paths-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 16 with probability 1/4; value 16 with probability 1/4; value 22 with probability 1/3; value 25 with probability 1/6. Sum masses for equal values. The candidate x is 41/2 units. Independently computed facts supplied for this question: exact weighted mean = 39/2; full set of modes = 16; full support = 16, 22, 25; probability of candidate x = 0. Statement: Under FI-1-duplicate-paths, the probability-weighted mean is 41/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 16 with probability 1/4; value 16 with probability 1/4; value 22 with probability 1/3; value 25 with probability 1/6. Sum masses for equal values. The candidate x is 41/2 units. Independently computed facts supplied for this question: exact weighted mean = 39/2; full set of modes = 16; full support = 16, 22, 25; probability of candidate x = 0. Statement: 41/2 units is mean-outcome(FI-1-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "queue delay",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-duplicate-paths-mean-outcome-False",
    "oracle": {
      "mean": "39/2",
      "modes": [
        "16"
      ],
      "x": "41/2",
      "masses": {
        "16": "1/2",
        "22": "1/3",
        "25": "1/6"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-duplicate-paths-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 16 with probability 1/4; value 16 with probability 1/4; value 22 with probability 1/3; value 25 with probability 1/6. Sum masses for equal values. The candidate x is 16 units. Independently computed facts supplied for this question: exact weighted mean = 39/2; full set of modes = 16; full support = 16, 22, 25; probability of candidate x = 1/2. Statement: Under FI-1-duplicate-paths, 16 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 16 with probability 1/4; value 16 with probability 1/4; value 22 with probability 1/3; value 25 with probability 1/6. Sum masses for equal values. The candidate x is 16 units. Independently computed facts supplied for this question: exact weighted mean = 39/2; full set of modes = 16; full support = 16, 22, 25; probability of candidate x = 1/2. Statement: 16 units is likeliest-outcome(FI-1-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "queue delay",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-duplicate-paths-likeliest-outcome-True",
    "oracle": {
      "mean": "39/2",
      "modes": [
        "16"
      ],
      "x": "16",
      "masses": {
        "16": "1/2",
        "22": "1/3",
        "25": "1/6"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-1-duplicate-paths-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 16 with probability 1/4; value 16 with probability 1/4; value 22 with probability 1/3; value 25 with probability 1/6. Sum masses for equal values. The candidate x is 22 units. Independently computed facts supplied for this question: exact weighted mean = 39/2; full set of modes = 16; full support = 16, 22, 25; probability of candidate x = 1/3. Statement: Under FI-1-duplicate-paths, 22 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional queue delay model FI-1-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 16 with probability 1/4; value 16 with probability 1/4; value 22 with probability 1/3; value 25 with probability 1/6. Sum masses for equal values. The candidate x is 22 units. Independently computed facts supplied for this question: exact weighted mean = 39/2; full set of modes = 16; full support = 16, 22, 25; probability of candidate x = 1/3. Statement: 22 units is likeliest-outcome(FI-1-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "queue delay",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "1-duplicate-paths-likeliest-outcome-False",
    "oracle": {
      "mean": "39/2",
      "modes": [
        "16"
      ],
      "x": "22",
      "masses": {
        "16": "1/2",
        "22": "1/3",
        "25": "1/6"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mean-outside-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/2; value 34 with probability 1/2. Sum masses for equal values. The candidate x is 31 units. Independently computed facts supplied for this question: exact weighted mean = 31; full set of modes = 28, 34; full support = 28, 34; probability of candidate x = 0. Statement: Under FI-2-mean-outside, the probability-weighted mean is 31 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/2; value 34 with probability 1/2. Sum masses for equal values. The candidate x is 31 units. Independently computed facts supplied for this question: exact weighted mean = 31; full set of modes = 28, 34; full support = 28, 34; probability of candidate x = 0. Statement: 31 units is mean-outcome(FI-2-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "retry count",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mean-outside-mean-outcome-True",
    "oracle": {
      "mean": "31",
      "modes": [
        "28",
        "34"
      ],
      "x": "31",
      "masses": {
        "28": "1/2",
        "34": "1/2"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mean-outside-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/2; value 34 with probability 1/2. Sum masses for equal values. The candidate x is 32 units. Independently computed facts supplied for this question: exact weighted mean = 31; full set of modes = 28, 34; full support = 28, 34; probability of candidate x = 0. Statement: Under FI-2-mean-outside, the probability-weighted mean is 32 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/2; value 34 with probability 1/2. Sum masses for equal values. The candidate x is 32 units. Independently computed facts supplied for this question: exact weighted mean = 31; full set of modes = 28, 34; full support = 28, 34; probability of candidate x = 0. Statement: 32 units is mean-outcome(FI-2-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "retry count",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mean-outside-mean-outcome-False",
    "oracle": {
      "mean": "31",
      "modes": [
        "28",
        "34"
      ],
      "x": "32",
      "masses": {
        "28": "1/2",
        "34": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mean-outside-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/2; value 34 with probability 1/2. Sum masses for equal values. The candidate x is 28 units. Independently computed facts supplied for this question: exact weighted mean = 31; full set of modes = 28, 34; full support = 28, 34; probability of candidate x = 1/2. Statement: Under FI-2-mean-outside, 28 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/2; value 34 with probability 1/2. Sum masses for equal values. The candidate x is 28 units. Independently computed facts supplied for this question: exact weighted mean = 31; full set of modes = 28, 34; full support = 28, 34; probability of candidate x = 1/2. Statement: 28 units is likeliest-outcome(FI-2-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "retry count",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mean-outside-likeliest-outcome-True",
    "oracle": {
      "mean": "31",
      "modes": [
        "28",
        "34"
      ],
      "x": "28",
      "masses": {
        "28": "1/2",
        "34": "1/2"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mean-outside-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/2; value 34 with probability 1/2. Sum masses for equal values. The candidate x is 27 units. Independently computed facts supplied for this question: exact weighted mean = 31; full set of modes = 28, 34; full support = 28, 34; probability of candidate x = 0. Statement: Under FI-2-mean-outside, 27 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/2; value 34 with probability 1/2. Sum masses for equal values. The candidate x is 27 units. Independently computed facts supplied for this question: exact weighted mean = 31; full set of modes = 28, 34; full support = 28, 34; probability of candidate x = 0. Statement: 27 units is likeliest-outcome(FI-2-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "retry count",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mean-outside-likeliest-outcome-False",
    "oracle": {
      "mean": "31",
      "modes": [
        "28",
        "34"
      ],
      "x": "27",
      "masses": {
        "28": "1/2",
        "34": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mode-below-half-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 32 with probability 3/10; value 38 with probability 3/10. Sum masses for equal values. The candidate x is 161/5 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28; full support = 28, 32, 38; probability of candidate x = 0. Statement: Under FI-2-mode-below-half, the probability-weighted mean is 161/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 32 with probability 3/10; value 38 with probability 3/10. Sum masses for equal values. The candidate x is 161/5 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28; full support = 28, 32, 38; probability of candidate x = 0. Statement: 161/5 units is mean-outcome(FI-2-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "retry count",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mode-below-half-mean-outcome-True",
    "oracle": {
      "mean": "161/5",
      "modes": [
        "28"
      ],
      "x": "161/5",
      "masses": {
        "28": "2/5",
        "32": "3/10",
        "38": "3/10"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mode-below-half-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 32 with probability 3/10; value 38 with probability 3/10. Sum masses for equal values. The candidate x is 166/5 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28; full support = 28, 32, 38; probability of candidate x = 0. Statement: Under FI-2-mode-below-half, the probability-weighted mean is 166/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 32 with probability 3/10; value 38 with probability 3/10. Sum masses for equal values. The candidate x is 166/5 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28; full support = 28, 32, 38; probability of candidate x = 0. Statement: 166/5 units is mean-outcome(FI-2-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "retry count",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mode-below-half-mean-outcome-False",
    "oracle": {
      "mean": "161/5",
      "modes": [
        "28"
      ],
      "x": "166/5",
      "masses": {
        "28": "2/5",
        "32": "3/10",
        "38": "3/10"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mode-below-half-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 32 with probability 3/10; value 38 with probability 3/10. Sum masses for equal values. The candidate x is 28 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28; full support = 28, 32, 38; probability of candidate x = 2/5. Statement: Under FI-2-mode-below-half, 28 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 32 with probability 3/10; value 38 with probability 3/10. Sum masses for equal values. The candidate x is 28 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28; full support = 28, 32, 38; probability of candidate x = 2/5. Statement: 28 units is likeliest-outcome(FI-2-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "retry count",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mode-below-half-likeliest-outcome-True",
    "oracle": {
      "mean": "161/5",
      "modes": [
        "28"
      ],
      "x": "28",
      "masses": {
        "28": "2/5",
        "32": "3/10",
        "38": "3/10"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mode-below-half-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 32 with probability 3/10; value 38 with probability 3/10. Sum masses for equal values. The candidate x is 27 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28; full support = 28, 32, 38; probability of candidate x = 0. Statement: Under FI-2-mode-below-half, 27 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 32 with probability 3/10; value 38 with probability 3/10. Sum masses for equal values. The candidate x is 27 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28; full support = 28, 32, 38; probability of candidate x = 0. Statement: 27 units is likeliest-outcome(FI-2-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "retry count",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mode-below-half-likeliest-outcome-False",
    "oracle": {
      "mean": "161/5",
      "modes": [
        "28"
      ],
      "x": "27",
      "masses": {
        "28": "2/5",
        "32": "3/10",
        "38": "3/10"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-tied-modes-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 34 with probability 2/5; value 37 with probability 1/5. Sum masses for equal values. The candidate x is 161/5 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28, 34; full support = 28, 34, 37; probability of candidate x = 0. Statement: Under FI-2-tied-modes, the probability-weighted mean is 161/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 34 with probability 2/5; value 37 with probability 1/5. Sum masses for equal values. The candidate x is 161/5 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28, 34; full support = 28, 34, 37; probability of candidate x = 0. Statement: 161/5 units is mean-outcome(FI-2-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "retry count",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-tied-modes-mean-outcome-True",
    "oracle": {
      "mean": "161/5",
      "modes": [
        "28",
        "34"
      ],
      "x": "161/5",
      "masses": {
        "28": "2/5",
        "34": "2/5",
        "37": "1/5"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-tied-modes-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 34 with probability 2/5; value 37 with probability 1/5. Sum masses for equal values. The candidate x is 166/5 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28, 34; full support = 28, 34, 37; probability of candidate x = 0. Statement: Under FI-2-tied-modes, the probability-weighted mean is 166/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 34 with probability 2/5; value 37 with probability 1/5. Sum masses for equal values. The candidate x is 166/5 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28, 34; full support = 28, 34, 37; probability of candidate x = 0. Statement: 166/5 units is mean-outcome(FI-2-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "retry count",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-tied-modes-mean-outcome-False",
    "oracle": {
      "mean": "161/5",
      "modes": [
        "28",
        "34"
      ],
      "x": "166/5",
      "masses": {
        "28": "2/5",
        "34": "2/5",
        "37": "1/5"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-tied-modes-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 34 with probability 2/5; value 37 with probability 1/5. Sum masses for equal values. The candidate x is 28 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28, 34; full support = 28, 34, 37; probability of candidate x = 2/5. Statement: Under FI-2-tied-modes, 28 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 34 with probability 2/5; value 37 with probability 1/5. Sum masses for equal values. The candidate x is 28 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28, 34; full support = 28, 34, 37; probability of candidate x = 2/5. Statement: 28 units is likeliest-outcome(FI-2-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "retry count",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-tied-modes-likeliest-outcome-True",
    "oracle": {
      "mean": "161/5",
      "modes": [
        "28",
        "34"
      ],
      "x": "28",
      "masses": {
        "28": "2/5",
        "34": "2/5",
        "37": "1/5"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-tied-modes-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 34 with probability 2/5; value 37 with probability 1/5. Sum masses for equal values. The candidate x is 27 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28, 34; full support = 28, 34, 37; probability of candidate x = 0. Statement: Under FI-2-tied-modes, 27 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 2/5; value 34 with probability 2/5; value 37 with probability 1/5. Sum masses for equal values. The candidate x is 27 units. Independently computed facts supplied for this question: exact weighted mean = 161/5; full set of modes = 28, 34; full support = 28, 34, 37; probability of candidate x = 0. Statement: 27 units is likeliest-outcome(FI-2-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "retry count",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-tied-modes-likeliest-outcome-False",
    "oracle": {
      "mean": "161/5",
      "modes": [
        "28",
        "34"
      ],
      "x": "27",
      "masses": {
        "28": "2/5",
        "34": "2/5",
        "37": "1/5"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mean-is-mode-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/4; value 32 with probability 1/2; value 36 with probability 1/4. Sum masses for equal values. The candidate x is 32 units. Independently computed facts supplied for this question: exact weighted mean = 32; full set of modes = 32; full support = 28, 32, 36; probability of candidate x = 1/2. Statement: Under FI-2-mean-is-mode, the probability-weighted mean is 32 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/4; value 32 with probability 1/2; value 36 with probability 1/4. Sum masses for equal values. The candidate x is 32 units. Independently computed facts supplied for this question: exact weighted mean = 32; full set of modes = 32; full support = 28, 32, 36; probability of candidate x = 1/2. Statement: 32 units is mean-outcome(FI-2-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "retry count",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mean-is-mode-mean-outcome-True",
    "oracle": {
      "mean": "32",
      "modes": [
        "32"
      ],
      "x": "32",
      "masses": {
        "28": "1/4",
        "32": "1/2",
        "36": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mean-is-mode-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/4; value 32 with probability 1/2; value 36 with probability 1/4. Sum masses for equal values. The candidate x is 33 units. Independently computed facts supplied for this question: exact weighted mean = 32; full set of modes = 32; full support = 28, 32, 36; probability of candidate x = 0. Statement: Under FI-2-mean-is-mode, the probability-weighted mean is 33 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/4; value 32 with probability 1/2; value 36 with probability 1/4. Sum masses for equal values. The candidate x is 33 units. Independently computed facts supplied for this question: exact weighted mean = 32; full set of modes = 32; full support = 28, 32, 36; probability of candidate x = 0. Statement: 33 units is mean-outcome(FI-2-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "retry count",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mean-is-mode-mean-outcome-False",
    "oracle": {
      "mean": "32",
      "modes": [
        "32"
      ],
      "x": "33",
      "masses": {
        "28": "1/4",
        "32": "1/2",
        "36": "1/4"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mean-is-mode-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/4; value 32 with probability 1/2; value 36 with probability 1/4. Sum masses for equal values. The candidate x is 32 units. Independently computed facts supplied for this question: exact weighted mean = 32; full set of modes = 32; full support = 28, 32, 36; probability of candidate x = 1/2. Statement: Under FI-2-mean-is-mode, 32 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/4; value 32 with probability 1/2; value 36 with probability 1/4. Sum masses for equal values. The candidate x is 32 units. Independently computed facts supplied for this question: exact weighted mean = 32; full set of modes = 32; full support = 28, 32, 36; probability of candidate x = 1/2. Statement: 32 units is likeliest-outcome(FI-2-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "retry count",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mean-is-mode-likeliest-outcome-True",
    "oracle": {
      "mean": "32",
      "modes": [
        "32"
      ],
      "x": "32",
      "masses": {
        "28": "1/4",
        "32": "1/2",
        "36": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-mean-is-mode-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/4; value 32 with probability 1/2; value 36 with probability 1/4. Sum masses for equal values. The candidate x is 27 units. Independently computed facts supplied for this question: exact weighted mean = 32; full set of modes = 32; full support = 28, 32, 36; probability of candidate x = 0. Statement: Under FI-2-mean-is-mode, 27 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 28 with probability 1/4; value 32 with probability 1/2; value 36 with probability 1/4. Sum masses for equal values. The candidate x is 27 units. Independently computed facts supplied for this question: exact weighted mean = 32; full set of modes = 32; full support = 28, 32, 36; probability of candidate x = 0. Statement: 27 units is likeliest-outcome(FI-2-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "retry count",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-mean-is-mode-likeliest-outcome-False",
    "oracle": {
      "mean": "32",
      "modes": [
        "32"
      ],
      "x": "27",
      "masses": {
        "28": "1/4",
        "32": "1/2",
        "36": "1/4"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-duplicate-paths-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 29 with probability 1/4; value 29 with probability 1/4; value 35 with probability 1/3; value 38 with probability 1/6. Sum masses for equal values. The candidate x is 65/2 units. Independently computed facts supplied for this question: exact weighted mean = 65/2; full set of modes = 29; full support = 29, 35, 38; probability of candidate x = 0. Statement: Under FI-2-duplicate-paths, the probability-weighted mean is 65/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 29 with probability 1/4; value 29 with probability 1/4; value 35 with probability 1/3; value 38 with probability 1/6. Sum masses for equal values. The candidate x is 65/2 units. Independently computed facts supplied for this question: exact weighted mean = 65/2; full set of modes = 29; full support = 29, 35, 38; probability of candidate x = 0. Statement: 65/2 units is mean-outcome(FI-2-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "retry count",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-duplicate-paths-mean-outcome-True",
    "oracle": {
      "mean": "65/2",
      "modes": [
        "29"
      ],
      "x": "65/2",
      "masses": {
        "29": "1/2",
        "35": "1/3",
        "38": "1/6"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-duplicate-paths-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 29 with probability 1/4; value 29 with probability 1/4; value 35 with probability 1/3; value 38 with probability 1/6. Sum masses for equal values. The candidate x is 67/2 units. Independently computed facts supplied for this question: exact weighted mean = 65/2; full set of modes = 29; full support = 29, 35, 38; probability of candidate x = 0. Statement: Under FI-2-duplicate-paths, the probability-weighted mean is 67/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 29 with probability 1/4; value 29 with probability 1/4; value 35 with probability 1/3; value 38 with probability 1/6. Sum masses for equal values. The candidate x is 67/2 units. Independently computed facts supplied for this question: exact weighted mean = 65/2; full set of modes = 29; full support = 29, 35, 38; probability of candidate x = 0. Statement: 67/2 units is mean-outcome(FI-2-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "retry count",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-duplicate-paths-mean-outcome-False",
    "oracle": {
      "mean": "65/2",
      "modes": [
        "29"
      ],
      "x": "67/2",
      "masses": {
        "29": "1/2",
        "35": "1/3",
        "38": "1/6"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-duplicate-paths-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 29 with probability 1/4; value 29 with probability 1/4; value 35 with probability 1/3; value 38 with probability 1/6. Sum masses for equal values. The candidate x is 29 units. Independently computed facts supplied for this question: exact weighted mean = 65/2; full set of modes = 29; full support = 29, 35, 38; probability of candidate x = 1/2. Statement: Under FI-2-duplicate-paths, 29 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 29 with probability 1/4; value 29 with probability 1/4; value 35 with probability 1/3; value 38 with probability 1/6. Sum masses for equal values. The candidate x is 29 units. Independently computed facts supplied for this question: exact weighted mean = 65/2; full set of modes = 29; full support = 29, 35, 38; probability of candidate x = 1/2. Statement: 29 units is likeliest-outcome(FI-2-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "retry count",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-duplicate-paths-likeliest-outcome-True",
    "oracle": {
      "mean": "65/2",
      "modes": [
        "29"
      ],
      "x": "29",
      "masses": {
        "29": "1/2",
        "35": "1/3",
        "38": "1/6"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-2-duplicate-paths-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 29 with probability 1/4; value 29 with probability 1/4; value 35 with probability 1/3; value 38 with probability 1/6. Sum masses for equal values. The candidate x is 28 units. Independently computed facts supplied for this question: exact weighted mean = 65/2; full set of modes = 29; full support = 29, 35, 38; probability of candidate x = 0. Statement: Under FI-2-duplicate-paths, 28 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional retry count model FI-2-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 29 with probability 1/4; value 29 with probability 1/4; value 35 with probability 1/3; value 38 with probability 1/6. Sum masses for equal values. The candidate x is 28 units. Independently computed facts supplied for this question: exact weighted mean = 65/2; full set of modes = 29; full support = 29, 35, 38; probability of candidate x = 0. Statement: 28 units is likeliest-outcome(FI-2-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "retry count",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "2-duplicate-paths-likeliest-outcome-False",
    "oracle": {
      "mean": "65/2",
      "modes": [
        "29"
      ],
      "x": "28",
      "masses": {
        "29": "1/2",
        "35": "1/3",
        "38": "1/6"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mean-outside-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/2; value 47 with probability 1/2. Sum masses for equal values. The candidate x is 44 units. Independently computed facts supplied for this question: exact weighted mean = 44; full set of modes = 41, 47; full support = 41, 47; probability of candidate x = 0. Statement: Under FI-3-mean-outside, the probability-weighted mean is 44 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/2; value 47 with probability 1/2. Sum masses for equal values. The candidate x is 44 units. Independently computed facts supplied for this question: exact weighted mean = 44; full set of modes = 41, 47; full support = 41, 47; probability of candidate x = 0. Statement: 44 units is mean-outcome(FI-3-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "resource use",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mean-outside-mean-outcome-True",
    "oracle": {
      "mean": "44",
      "modes": [
        "41",
        "47"
      ],
      "x": "44",
      "masses": {
        "41": "1/2",
        "47": "1/2"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mean-outside-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/2; value 47 with probability 1/2. Sum masses for equal values. The candidate x is 45 units. Independently computed facts supplied for this question: exact weighted mean = 44; full set of modes = 41, 47; full support = 41, 47; probability of candidate x = 0. Statement: Under FI-3-mean-outside, the probability-weighted mean is 45 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/2; value 47 with probability 1/2. Sum masses for equal values. The candidate x is 45 units. Independently computed facts supplied for this question: exact weighted mean = 44; full set of modes = 41, 47; full support = 41, 47; probability of candidate x = 0. Statement: 45 units is mean-outcome(FI-3-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "resource use",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mean-outside-mean-outcome-False",
    "oracle": {
      "mean": "44",
      "modes": [
        "41",
        "47"
      ],
      "x": "45",
      "masses": {
        "41": "1/2",
        "47": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mean-outside-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/2; value 47 with probability 1/2. Sum masses for equal values. The candidate x is 47 units. Independently computed facts supplied for this question: exact weighted mean = 44; full set of modes = 41, 47; full support = 41, 47; probability of candidate x = 1/2. Statement: Under FI-3-mean-outside, 47 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/2; value 47 with probability 1/2. Sum masses for equal values. The candidate x is 47 units. Independently computed facts supplied for this question: exact weighted mean = 44; full set of modes = 41, 47; full support = 41, 47; probability of candidate x = 1/2. Statement: 47 units is likeliest-outcome(FI-3-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "resource use",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mean-outside-likeliest-outcome-True",
    "oracle": {
      "mean": "44",
      "modes": [
        "41",
        "47"
      ],
      "x": "47",
      "masses": {
        "41": "1/2",
        "47": "1/2"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mean-outside-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/2; value 47 with probability 1/2. Sum masses for equal values. The candidate x is 40 units. Independently computed facts supplied for this question: exact weighted mean = 44; full set of modes = 41, 47; full support = 41, 47; probability of candidate x = 0. Statement: Under FI-3-mean-outside, 40 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/2; value 47 with probability 1/2. Sum masses for equal values. The candidate x is 40 units. Independently computed facts supplied for this question: exact weighted mean = 44; full set of modes = 41, 47; full support = 41, 47; probability of candidate x = 0. Statement: 40 units is likeliest-outcome(FI-3-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "resource use",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mean-outside-likeliest-outcome-False",
    "oracle": {
      "mean": "44",
      "modes": [
        "41",
        "47"
      ],
      "x": "40",
      "masses": {
        "41": "1/2",
        "47": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mode-below-half-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 45 with probability 3/10; value 51 with probability 3/10. Sum masses for equal values. The candidate x is 226/5 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41; full support = 41, 45, 51; probability of candidate x = 0. Statement: Under FI-3-mode-below-half, the probability-weighted mean is 226/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 45 with probability 3/10; value 51 with probability 3/10. Sum masses for equal values. The candidate x is 226/5 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41; full support = 41, 45, 51; probability of candidate x = 0. Statement: 226/5 units is mean-outcome(FI-3-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "resource use",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mode-below-half-mean-outcome-True",
    "oracle": {
      "mean": "226/5",
      "modes": [
        "41"
      ],
      "x": "226/5",
      "masses": {
        "41": "2/5",
        "45": "3/10",
        "51": "3/10"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mode-below-half-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 45 with probability 3/10; value 51 with probability 3/10. Sum masses for equal values. The candidate x is 231/5 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41; full support = 41, 45, 51; probability of candidate x = 0. Statement: Under FI-3-mode-below-half, the probability-weighted mean is 231/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 45 with probability 3/10; value 51 with probability 3/10. Sum masses for equal values. The candidate x is 231/5 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41; full support = 41, 45, 51; probability of candidate x = 0. Statement: 231/5 units is mean-outcome(FI-3-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "resource use",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mode-below-half-mean-outcome-False",
    "oracle": {
      "mean": "226/5",
      "modes": [
        "41"
      ],
      "x": "231/5",
      "masses": {
        "41": "2/5",
        "45": "3/10",
        "51": "3/10"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mode-below-half-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 45 with probability 3/10; value 51 with probability 3/10. Sum masses for equal values. The candidate x is 41 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41; full support = 41, 45, 51; probability of candidate x = 2/5. Statement: Under FI-3-mode-below-half, 41 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 45 with probability 3/10; value 51 with probability 3/10. Sum masses for equal values. The candidate x is 41 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41; full support = 41, 45, 51; probability of candidate x = 2/5. Statement: 41 units is likeliest-outcome(FI-3-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "resource use",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mode-below-half-likeliest-outcome-True",
    "oracle": {
      "mean": "226/5",
      "modes": [
        "41"
      ],
      "x": "41",
      "masses": {
        "41": "2/5",
        "45": "3/10",
        "51": "3/10"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mode-below-half-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 45 with probability 3/10; value 51 with probability 3/10. Sum masses for equal values. The candidate x is 45 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41; full support = 41, 45, 51; probability of candidate x = 3/10. Statement: Under FI-3-mode-below-half, 45 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 45 with probability 3/10; value 51 with probability 3/10. Sum masses for equal values. The candidate x is 45 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41; full support = 41, 45, 51; probability of candidate x = 3/10. Statement: 45 units is likeliest-outcome(FI-3-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "resource use",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mode-below-half-likeliest-outcome-False",
    "oracle": {
      "mean": "226/5",
      "modes": [
        "41"
      ],
      "x": "45",
      "masses": {
        "41": "2/5",
        "45": "3/10",
        "51": "3/10"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-tied-modes-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 47 with probability 2/5; value 50 with probability 1/5. Sum masses for equal values. The candidate x is 226/5 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41, 47; full support = 41, 47, 50; probability of candidate x = 0. Statement: Under FI-3-tied-modes, the probability-weighted mean is 226/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 47 with probability 2/5; value 50 with probability 1/5. Sum masses for equal values. The candidate x is 226/5 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41, 47; full support = 41, 47, 50; probability of candidate x = 0. Statement: 226/5 units is mean-outcome(FI-3-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "resource use",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-tied-modes-mean-outcome-True",
    "oracle": {
      "mean": "226/5",
      "modes": [
        "41",
        "47"
      ],
      "x": "226/5",
      "masses": {
        "41": "2/5",
        "47": "2/5",
        "50": "1/5"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-tied-modes-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 47 with probability 2/5; value 50 with probability 1/5. Sum masses for equal values. The candidate x is 231/5 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41, 47; full support = 41, 47, 50; probability of candidate x = 0. Statement: Under FI-3-tied-modes, the probability-weighted mean is 231/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 47 with probability 2/5; value 50 with probability 1/5. Sum masses for equal values. The candidate x is 231/5 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41, 47; full support = 41, 47, 50; probability of candidate x = 0. Statement: 231/5 units is mean-outcome(FI-3-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "resource use",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-tied-modes-mean-outcome-False",
    "oracle": {
      "mean": "226/5",
      "modes": [
        "41",
        "47"
      ],
      "x": "231/5",
      "masses": {
        "41": "2/5",
        "47": "2/5",
        "50": "1/5"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-tied-modes-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 47 with probability 2/5; value 50 with probability 1/5. Sum masses for equal values. The candidate x is 47 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41, 47; full support = 41, 47, 50; probability of candidate x = 2/5. Statement: Under FI-3-tied-modes, 47 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 47 with probability 2/5; value 50 with probability 1/5. Sum masses for equal values. The candidate x is 47 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41, 47; full support = 41, 47, 50; probability of candidate x = 2/5. Statement: 47 units is likeliest-outcome(FI-3-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "resource use",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-tied-modes-likeliest-outcome-True",
    "oracle": {
      "mean": "226/5",
      "modes": [
        "41",
        "47"
      ],
      "x": "47",
      "masses": {
        "41": "2/5",
        "47": "2/5",
        "50": "1/5"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-tied-modes-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 47 with probability 2/5; value 50 with probability 1/5. Sum masses for equal values. The candidate x is 50 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41, 47; full support = 41, 47, 50; probability of candidate x = 1/5. Statement: Under FI-3-tied-modes, 50 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 2/5; value 47 with probability 2/5; value 50 with probability 1/5. Sum masses for equal values. The candidate x is 50 units. Independently computed facts supplied for this question: exact weighted mean = 226/5; full set of modes = 41, 47; full support = 41, 47, 50; probability of candidate x = 1/5. Statement: 50 units is likeliest-outcome(FI-3-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "resource use",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-tied-modes-likeliest-outcome-False",
    "oracle": {
      "mean": "226/5",
      "modes": [
        "41",
        "47"
      ],
      "x": "50",
      "masses": {
        "41": "2/5",
        "47": "2/5",
        "50": "1/5"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mean-is-mode-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/4; value 45 with probability 1/2; value 49 with probability 1/4. Sum masses for equal values. The candidate x is 45 units. Independently computed facts supplied for this question: exact weighted mean = 45; full set of modes = 45; full support = 41, 45, 49; probability of candidate x = 1/2. Statement: Under FI-3-mean-is-mode, the probability-weighted mean is 45 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/4; value 45 with probability 1/2; value 49 with probability 1/4. Sum masses for equal values. The candidate x is 45 units. Independently computed facts supplied for this question: exact weighted mean = 45; full set of modes = 45; full support = 41, 45, 49; probability of candidate x = 1/2. Statement: 45 units is mean-outcome(FI-3-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "resource use",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mean-is-mode-mean-outcome-True",
    "oracle": {
      "mean": "45",
      "modes": [
        "45"
      ],
      "x": "45",
      "masses": {
        "41": "1/4",
        "45": "1/2",
        "49": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mean-is-mode-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/4; value 45 with probability 1/2; value 49 with probability 1/4. Sum masses for equal values. The candidate x is 46 units. Independently computed facts supplied for this question: exact weighted mean = 45; full set of modes = 45; full support = 41, 45, 49; probability of candidate x = 0. Statement: Under FI-3-mean-is-mode, the probability-weighted mean is 46 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/4; value 45 with probability 1/2; value 49 with probability 1/4. Sum masses for equal values. The candidate x is 46 units. Independently computed facts supplied for this question: exact weighted mean = 45; full set of modes = 45; full support = 41, 45, 49; probability of candidate x = 0. Statement: 46 units is mean-outcome(FI-3-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "resource use",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mean-is-mode-mean-outcome-False",
    "oracle": {
      "mean": "45",
      "modes": [
        "45"
      ],
      "x": "46",
      "masses": {
        "41": "1/4",
        "45": "1/2",
        "49": "1/4"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mean-is-mode-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/4; value 45 with probability 1/2; value 49 with probability 1/4. Sum masses for equal values. The candidate x is 45 units. Independently computed facts supplied for this question: exact weighted mean = 45; full set of modes = 45; full support = 41, 45, 49; probability of candidate x = 1/2. Statement: Under FI-3-mean-is-mode, 45 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/4; value 45 with probability 1/2; value 49 with probability 1/4. Sum masses for equal values. The candidate x is 45 units. Independently computed facts supplied for this question: exact weighted mean = 45; full set of modes = 45; full support = 41, 45, 49; probability of candidate x = 1/2. Statement: 45 units is likeliest-outcome(FI-3-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "resource use",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mean-is-mode-likeliest-outcome-True",
    "oracle": {
      "mean": "45",
      "modes": [
        "45"
      ],
      "x": "45",
      "masses": {
        "41": "1/4",
        "45": "1/2",
        "49": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-mean-is-mode-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/4; value 45 with probability 1/2; value 49 with probability 1/4. Sum masses for equal values. The candidate x is 41 units. Independently computed facts supplied for this question: exact weighted mean = 45; full set of modes = 45; full support = 41, 45, 49; probability of candidate x = 1/4. Statement: Under FI-3-mean-is-mode, 41 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 41 with probability 1/4; value 45 with probability 1/2; value 49 with probability 1/4. Sum masses for equal values. The candidate x is 41 units. Independently computed facts supplied for this question: exact weighted mean = 45; full set of modes = 45; full support = 41, 45, 49; probability of candidate x = 1/4. Statement: 41 units is likeliest-outcome(FI-3-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "resource use",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-mean-is-mode-likeliest-outcome-False",
    "oracle": {
      "mean": "45",
      "modes": [
        "45"
      ],
      "x": "41",
      "masses": {
        "41": "1/4",
        "45": "1/2",
        "49": "1/4"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-duplicate-paths-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 42 with probability 1/4; value 42 with probability 1/4; value 48 with probability 1/3; value 51 with probability 1/6. Sum masses for equal values. The candidate x is 91/2 units. Independently computed facts supplied for this question: exact weighted mean = 91/2; full set of modes = 42; full support = 42, 48, 51; probability of candidate x = 0. Statement: Under FI-3-duplicate-paths, the probability-weighted mean is 91/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 42 with probability 1/4; value 42 with probability 1/4; value 48 with probability 1/3; value 51 with probability 1/6. Sum masses for equal values. The candidate x is 91/2 units. Independently computed facts supplied for this question: exact weighted mean = 91/2; full set of modes = 42; full support = 42, 48, 51; probability of candidate x = 0. Statement: 91/2 units is mean-outcome(FI-3-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "resource use",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-duplicate-paths-mean-outcome-True",
    "oracle": {
      "mean": "91/2",
      "modes": [
        "42"
      ],
      "x": "91/2",
      "masses": {
        "42": "1/2",
        "48": "1/3",
        "51": "1/6"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-duplicate-paths-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 42 with probability 1/4; value 42 with probability 1/4; value 48 with probability 1/3; value 51 with probability 1/6. Sum masses for equal values. The candidate x is 93/2 units. Independently computed facts supplied for this question: exact weighted mean = 91/2; full set of modes = 42; full support = 42, 48, 51; probability of candidate x = 0. Statement: Under FI-3-duplicate-paths, the probability-weighted mean is 93/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 42 with probability 1/4; value 42 with probability 1/4; value 48 with probability 1/3; value 51 with probability 1/6. Sum masses for equal values. The candidate x is 93/2 units. Independently computed facts supplied for this question: exact weighted mean = 91/2; full set of modes = 42; full support = 42, 48, 51; probability of candidate x = 0. Statement: 93/2 units is mean-outcome(FI-3-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "resource use",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-duplicate-paths-mean-outcome-False",
    "oracle": {
      "mean": "91/2",
      "modes": [
        "42"
      ],
      "x": "93/2",
      "masses": {
        "42": "1/2",
        "48": "1/3",
        "51": "1/6"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-duplicate-paths-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 42 with probability 1/4; value 42 with probability 1/4; value 48 with probability 1/3; value 51 with probability 1/6. Sum masses for equal values. The candidate x is 42 units. Independently computed facts supplied for this question: exact weighted mean = 91/2; full set of modes = 42; full support = 42, 48, 51; probability of candidate x = 1/2. Statement: Under FI-3-duplicate-paths, 42 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 42 with probability 1/4; value 42 with probability 1/4; value 48 with probability 1/3; value 51 with probability 1/6. Sum masses for equal values. The candidate x is 42 units. Independently computed facts supplied for this question: exact weighted mean = 91/2; full set of modes = 42; full support = 42, 48, 51; probability of candidate x = 1/2. Statement: 42 units is likeliest-outcome(FI-3-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "resource use",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-duplicate-paths-likeliest-outcome-True",
    "oracle": {
      "mean": "91/2",
      "modes": [
        "42"
      ],
      "x": "42",
      "masses": {
        "42": "1/2",
        "48": "1/3",
        "51": "1/6"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-3-duplicate-paths-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 42 with probability 1/4; value 42 with probability 1/4; value 48 with probability 1/3; value 51 with probability 1/6. Sum masses for equal values. The candidate x is 48 units. Independently computed facts supplied for this question: exact weighted mean = 91/2; full set of modes = 42; full support = 42, 48, 51; probability of candidate x = 1/3. Statement: Under FI-3-duplicate-paths, 48 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional resource use model FI-3-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 42 with probability 1/4; value 42 with probability 1/4; value 48 with probability 1/3; value 51 with probability 1/6. Sum masses for equal values. The candidate x is 48 units. Independently computed facts supplied for this question: exact weighted mean = 91/2; full set of modes = 42; full support = 42, 48, 51; probability of candidate x = 1/3. Statement: 48 units is likeliest-outcome(FI-3-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "resource use",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "3-duplicate-paths-likeliest-outcome-False",
    "oracle": {
      "mean": "91/2",
      "modes": [
        "42"
      ],
      "x": "48",
      "masses": {
        "42": "1/2",
        "48": "1/3",
        "51": "1/6"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mean-outside-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/2; value 60 with probability 1/2. Sum masses for equal values. The candidate x is 57 units. Independently computed facts supplied for this question: exact weighted mean = 57; full set of modes = 54, 60; full support = 54, 60; probability of candidate x = 0. Statement: Under FI-4-mean-outside, the probability-weighted mean is 57 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/2; value 60 with probability 1/2. Sum masses for equal values. The candidate x is 57 units. Independently computed facts supplied for this question: exact weighted mean = 57; full set of modes = 54, 60; full support = 54, 60; probability of candidate x = 0. Statement: 57 units is mean-outcome(FI-4-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "simulated inventory",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mean-outside-mean-outcome-True",
    "oracle": {
      "mean": "57",
      "modes": [
        "54",
        "60"
      ],
      "x": "57",
      "masses": {
        "54": "1/2",
        "60": "1/2"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mean-outside-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/2; value 60 with probability 1/2. Sum masses for equal values. The candidate x is 58 units. Independently computed facts supplied for this question: exact weighted mean = 57; full set of modes = 54, 60; full support = 54, 60; probability of candidate x = 0. Statement: Under FI-4-mean-outside, the probability-weighted mean is 58 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/2; value 60 with probability 1/2. Sum masses for equal values. The candidate x is 58 units. Independently computed facts supplied for this question: exact weighted mean = 57; full set of modes = 54, 60; full support = 54, 60; probability of candidate x = 0. Statement: 58 units is mean-outcome(FI-4-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "simulated inventory",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mean-outside-mean-outcome-False",
    "oracle": {
      "mean": "57",
      "modes": [
        "54",
        "60"
      ],
      "x": "58",
      "masses": {
        "54": "1/2",
        "60": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mean-outside-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/2; value 60 with probability 1/2. Sum masses for equal values. The candidate x is 54 units. Independently computed facts supplied for this question: exact weighted mean = 57; full set of modes = 54, 60; full support = 54, 60; probability of candidate x = 1/2. Statement: Under FI-4-mean-outside, 54 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/2; value 60 with probability 1/2. Sum masses for equal values. The candidate x is 54 units. Independently computed facts supplied for this question: exact weighted mean = 57; full set of modes = 54, 60; full support = 54, 60; probability of candidate x = 1/2. Statement: 54 units is likeliest-outcome(FI-4-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "simulated inventory",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mean-outside-likeliest-outcome-True",
    "oracle": {
      "mean": "57",
      "modes": [
        "54",
        "60"
      ],
      "x": "54",
      "masses": {
        "54": "1/2",
        "60": "1/2"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mean-outside-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/2; value 60 with probability 1/2. Sum masses for equal values. The candidate x is 53 units. Independently computed facts supplied for this question: exact weighted mean = 57; full set of modes = 54, 60; full support = 54, 60; probability of candidate x = 0. Statement: Under FI-4-mean-outside, 53 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/2; value 60 with probability 1/2. Sum masses for equal values. The candidate x is 53 units. Independently computed facts supplied for this question: exact weighted mean = 57; full set of modes = 54, 60; full support = 54, 60; probability of candidate x = 0. Statement: 53 units is likeliest-outcome(FI-4-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "simulated inventory",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mean-outside-likeliest-outcome-False",
    "oracle": {
      "mean": "57",
      "modes": [
        "54",
        "60"
      ],
      "x": "53",
      "masses": {
        "54": "1/2",
        "60": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mode-below-half-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 58 with probability 3/10; value 64 with probability 3/10. Sum masses for equal values. The candidate x is 291/5 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54; full support = 54, 58, 64; probability of candidate x = 0. Statement: Under FI-4-mode-below-half, the probability-weighted mean is 291/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 58 with probability 3/10; value 64 with probability 3/10. Sum masses for equal values. The candidate x is 291/5 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54; full support = 54, 58, 64; probability of candidate x = 0. Statement: 291/5 units is mean-outcome(FI-4-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "simulated inventory",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mode-below-half-mean-outcome-True",
    "oracle": {
      "mean": "291/5",
      "modes": [
        "54"
      ],
      "x": "291/5",
      "masses": {
        "54": "2/5",
        "58": "3/10",
        "64": "3/10"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mode-below-half-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 58 with probability 3/10; value 64 with probability 3/10. Sum masses for equal values. The candidate x is 296/5 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54; full support = 54, 58, 64; probability of candidate x = 0. Statement: Under FI-4-mode-below-half, the probability-weighted mean is 296/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 58 with probability 3/10; value 64 with probability 3/10. Sum masses for equal values. The candidate x is 296/5 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54; full support = 54, 58, 64; probability of candidate x = 0. Statement: 296/5 units is mean-outcome(FI-4-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "simulated inventory",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mode-below-half-mean-outcome-False",
    "oracle": {
      "mean": "291/5",
      "modes": [
        "54"
      ],
      "x": "296/5",
      "masses": {
        "54": "2/5",
        "58": "3/10",
        "64": "3/10"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mode-below-half-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 58 with probability 3/10; value 64 with probability 3/10. Sum masses for equal values. The candidate x is 54 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54; full support = 54, 58, 64; probability of candidate x = 2/5. Statement: Under FI-4-mode-below-half, 54 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 58 with probability 3/10; value 64 with probability 3/10. Sum masses for equal values. The candidate x is 54 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54; full support = 54, 58, 64; probability of candidate x = 2/5. Statement: 54 units is likeliest-outcome(FI-4-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "simulated inventory",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mode-below-half-likeliest-outcome-True",
    "oracle": {
      "mean": "291/5",
      "modes": [
        "54"
      ],
      "x": "54",
      "masses": {
        "54": "2/5",
        "58": "3/10",
        "64": "3/10"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mode-below-half-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 58 with probability 3/10; value 64 with probability 3/10. Sum masses for equal values. The candidate x is 53 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54; full support = 54, 58, 64; probability of candidate x = 0. Statement: Under FI-4-mode-below-half, 53 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 58 with probability 3/10; value 64 with probability 3/10. Sum masses for equal values. The candidate x is 53 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54; full support = 54, 58, 64; probability of candidate x = 0. Statement: 53 units is likeliest-outcome(FI-4-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "simulated inventory",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mode-below-half-likeliest-outcome-False",
    "oracle": {
      "mean": "291/5",
      "modes": [
        "54"
      ],
      "x": "53",
      "masses": {
        "54": "2/5",
        "58": "3/10",
        "64": "3/10"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-tied-modes-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 60 with probability 2/5; value 63 with probability 1/5. Sum masses for equal values. The candidate x is 291/5 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54, 60; full support = 54, 60, 63; probability of candidate x = 0. Statement: Under FI-4-tied-modes, the probability-weighted mean is 291/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 60 with probability 2/5; value 63 with probability 1/5. Sum masses for equal values. The candidate x is 291/5 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54, 60; full support = 54, 60, 63; probability of candidate x = 0. Statement: 291/5 units is mean-outcome(FI-4-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "simulated inventory",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-tied-modes-mean-outcome-True",
    "oracle": {
      "mean": "291/5",
      "modes": [
        "54",
        "60"
      ],
      "x": "291/5",
      "masses": {
        "54": "2/5",
        "60": "2/5",
        "63": "1/5"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-tied-modes-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 60 with probability 2/5; value 63 with probability 1/5. Sum masses for equal values. The candidate x is 296/5 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54, 60; full support = 54, 60, 63; probability of candidate x = 0. Statement: Under FI-4-tied-modes, the probability-weighted mean is 296/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 60 with probability 2/5; value 63 with probability 1/5. Sum masses for equal values. The candidate x is 296/5 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54, 60; full support = 54, 60, 63; probability of candidate x = 0. Statement: 296/5 units is mean-outcome(FI-4-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "simulated inventory",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-tied-modes-mean-outcome-False",
    "oracle": {
      "mean": "291/5",
      "modes": [
        "54",
        "60"
      ],
      "x": "296/5",
      "masses": {
        "54": "2/5",
        "60": "2/5",
        "63": "1/5"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-tied-modes-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 60 with probability 2/5; value 63 with probability 1/5. Sum masses for equal values. The candidate x is 54 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54, 60; full support = 54, 60, 63; probability of candidate x = 2/5. Statement: Under FI-4-tied-modes, 54 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 60 with probability 2/5; value 63 with probability 1/5. Sum masses for equal values. The candidate x is 54 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54, 60; full support = 54, 60, 63; probability of candidate x = 2/5. Statement: 54 units is likeliest-outcome(FI-4-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "simulated inventory",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-tied-modes-likeliest-outcome-True",
    "oracle": {
      "mean": "291/5",
      "modes": [
        "54",
        "60"
      ],
      "x": "54",
      "masses": {
        "54": "2/5",
        "60": "2/5",
        "63": "1/5"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-tied-modes-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 60 with probability 2/5; value 63 with probability 1/5. Sum masses for equal values. The candidate x is 53 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54, 60; full support = 54, 60, 63; probability of candidate x = 0. Statement: Under FI-4-tied-modes, 53 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 2/5; value 60 with probability 2/5; value 63 with probability 1/5. Sum masses for equal values. The candidate x is 53 units. Independently computed facts supplied for this question: exact weighted mean = 291/5; full set of modes = 54, 60; full support = 54, 60, 63; probability of candidate x = 0. Statement: 53 units is likeliest-outcome(FI-4-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "simulated inventory",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-tied-modes-likeliest-outcome-False",
    "oracle": {
      "mean": "291/5",
      "modes": [
        "54",
        "60"
      ],
      "x": "53",
      "masses": {
        "54": "2/5",
        "60": "2/5",
        "63": "1/5"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mean-is-mode-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/4; value 58 with probability 1/2; value 62 with probability 1/4. Sum masses for equal values. The candidate x is 58 units. Independently computed facts supplied for this question: exact weighted mean = 58; full set of modes = 58; full support = 54, 58, 62; probability of candidate x = 1/2. Statement: Under FI-4-mean-is-mode, the probability-weighted mean is 58 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/4; value 58 with probability 1/2; value 62 with probability 1/4. Sum masses for equal values. The candidate x is 58 units. Independently computed facts supplied for this question: exact weighted mean = 58; full set of modes = 58; full support = 54, 58, 62; probability of candidate x = 1/2. Statement: 58 units is mean-outcome(FI-4-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "simulated inventory",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mean-is-mode-mean-outcome-True",
    "oracle": {
      "mean": "58",
      "modes": [
        "58"
      ],
      "x": "58",
      "masses": {
        "54": "1/4",
        "58": "1/2",
        "62": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mean-is-mode-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/4; value 58 with probability 1/2; value 62 with probability 1/4. Sum masses for equal values. The candidate x is 59 units. Independently computed facts supplied for this question: exact weighted mean = 58; full set of modes = 58; full support = 54, 58, 62; probability of candidate x = 0. Statement: Under FI-4-mean-is-mode, the probability-weighted mean is 59 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/4; value 58 with probability 1/2; value 62 with probability 1/4. Sum masses for equal values. The candidate x is 59 units. Independently computed facts supplied for this question: exact weighted mean = 58; full set of modes = 58; full support = 54, 58, 62; probability of candidate x = 0. Statement: 59 units is mean-outcome(FI-4-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "simulated inventory",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mean-is-mode-mean-outcome-False",
    "oracle": {
      "mean": "58",
      "modes": [
        "58"
      ],
      "x": "59",
      "masses": {
        "54": "1/4",
        "58": "1/2",
        "62": "1/4"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mean-is-mode-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/4; value 58 with probability 1/2; value 62 with probability 1/4. Sum masses for equal values. The candidate x is 58 units. Independently computed facts supplied for this question: exact weighted mean = 58; full set of modes = 58; full support = 54, 58, 62; probability of candidate x = 1/2. Statement: Under FI-4-mean-is-mode, 58 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/4; value 58 with probability 1/2; value 62 with probability 1/4. Sum masses for equal values. The candidate x is 58 units. Independently computed facts supplied for this question: exact weighted mean = 58; full set of modes = 58; full support = 54, 58, 62; probability of candidate x = 1/2. Statement: 58 units is likeliest-outcome(FI-4-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "simulated inventory",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mean-is-mode-likeliest-outcome-True",
    "oracle": {
      "mean": "58",
      "modes": [
        "58"
      ],
      "x": "58",
      "masses": {
        "54": "1/4",
        "58": "1/2",
        "62": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-mean-is-mode-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/4; value 58 with probability 1/2; value 62 with probability 1/4. Sum masses for equal values. The candidate x is 53 units. Independently computed facts supplied for this question: exact weighted mean = 58; full set of modes = 58; full support = 54, 58, 62; probability of candidate x = 0. Statement: Under FI-4-mean-is-mode, 53 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 54 with probability 1/4; value 58 with probability 1/2; value 62 with probability 1/4. Sum masses for equal values. The candidate x is 53 units. Independently computed facts supplied for this question: exact weighted mean = 58; full set of modes = 58; full support = 54, 58, 62; probability of candidate x = 0. Statement: 53 units is likeliest-outcome(FI-4-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "simulated inventory",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-mean-is-mode-likeliest-outcome-False",
    "oracle": {
      "mean": "58",
      "modes": [
        "58"
      ],
      "x": "53",
      "masses": {
        "54": "1/4",
        "58": "1/2",
        "62": "1/4"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-duplicate-paths-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 55 with probability 1/4; value 55 with probability 1/4; value 61 with probability 1/3; value 64 with probability 1/6. Sum masses for equal values. The candidate x is 117/2 units. Independently computed facts supplied for this question: exact weighted mean = 117/2; full set of modes = 55; full support = 55, 61, 64; probability of candidate x = 0. Statement: Under FI-4-duplicate-paths, the probability-weighted mean is 117/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 55 with probability 1/4; value 55 with probability 1/4; value 61 with probability 1/3; value 64 with probability 1/6. Sum masses for equal values. The candidate x is 117/2 units. Independently computed facts supplied for this question: exact weighted mean = 117/2; full set of modes = 55; full support = 55, 61, 64; probability of candidate x = 0. Statement: 117/2 units is mean-outcome(FI-4-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "simulated inventory",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-duplicate-paths-mean-outcome-True",
    "oracle": {
      "mean": "117/2",
      "modes": [
        "55"
      ],
      "x": "117/2",
      "masses": {
        "55": "1/2",
        "61": "1/3",
        "64": "1/6"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-duplicate-paths-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 55 with probability 1/4; value 55 with probability 1/4; value 61 with probability 1/3; value 64 with probability 1/6. Sum masses for equal values. The candidate x is 119/2 units. Independently computed facts supplied for this question: exact weighted mean = 117/2; full set of modes = 55; full support = 55, 61, 64; probability of candidate x = 0. Statement: Under FI-4-duplicate-paths, the probability-weighted mean is 119/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 55 with probability 1/4; value 55 with probability 1/4; value 61 with probability 1/3; value 64 with probability 1/6. Sum masses for equal values. The candidate x is 119/2 units. Independently computed facts supplied for this question: exact weighted mean = 117/2; full set of modes = 55; full support = 55, 61, 64; probability of candidate x = 0. Statement: 119/2 units is mean-outcome(FI-4-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "simulated inventory",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-duplicate-paths-mean-outcome-False",
    "oracle": {
      "mean": "117/2",
      "modes": [
        "55"
      ],
      "x": "119/2",
      "masses": {
        "55": "1/2",
        "61": "1/3",
        "64": "1/6"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-duplicate-paths-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 55 with probability 1/4; value 55 with probability 1/4; value 61 with probability 1/3; value 64 with probability 1/6. Sum masses for equal values. The candidate x is 55 units. Independently computed facts supplied for this question: exact weighted mean = 117/2; full set of modes = 55; full support = 55, 61, 64; probability of candidate x = 1/2. Statement: Under FI-4-duplicate-paths, 55 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 55 with probability 1/4; value 55 with probability 1/4; value 61 with probability 1/3; value 64 with probability 1/6. Sum masses for equal values. The candidate x is 55 units. Independently computed facts supplied for this question: exact weighted mean = 117/2; full set of modes = 55; full support = 55, 61, 64; probability of candidate x = 1/2. Statement: 55 units is likeliest-outcome(FI-4-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "simulated inventory",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-duplicate-paths-likeliest-outcome-True",
    "oracle": {
      "mean": "117/2",
      "modes": [
        "55"
      ],
      "x": "55",
      "masses": {
        "55": "1/2",
        "61": "1/3",
        "64": "1/6"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-4-duplicate-paths-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 55 with probability 1/4; value 55 with probability 1/4; value 61 with probability 1/3; value 64 with probability 1/6. Sum masses for equal values. The candidate x is 54 units. Independently computed facts supplied for this question: exact weighted mean = 117/2; full set of modes = 55; full support = 55, 61, 64; probability of candidate x = 0. Statement: Under FI-4-duplicate-paths, 54 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional simulated inventory model FI-4-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 55 with probability 1/4; value 55 with probability 1/4; value 61 with probability 1/3; value 64 with probability 1/6. Sum masses for equal values. The candidate x is 54 units. Independently computed facts supplied for this question: exact weighted mean = 117/2; full set of modes = 55; full support = 55, 61, 64; probability of candidate x = 0. Statement: 54 units is likeliest-outcome(FI-4-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "simulated inventory",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "4-duplicate-paths-likeliest-outcome-False",
    "oracle": {
      "mean": "117/2",
      "modes": [
        "55"
      ],
      "x": "54",
      "masses": {
        "55": "1/2",
        "61": "1/3",
        "64": "1/6"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mean-outside-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/2; value 73 with probability 1/2. Sum masses for equal values. The candidate x is 70 units. Independently computed facts supplied for this question: exact weighted mean = 70; full set of modes = 67, 73; full support = 67, 73; probability of candidate x = 0. Statement: Under FI-5-mean-outside, the probability-weighted mean is 70 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/2; value 73 with probability 1/2. Sum masses for equal values. The candidate x is 70 units. Independently computed facts supplied for this question: exact weighted mean = 70; full set of modes = 67, 73; full support = 67, 73; probability of candidate x = 0. Statement: 70 units is mean-outcome(FI-5-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "batch size",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mean-outside-mean-outcome-True",
    "oracle": {
      "mean": "70",
      "modes": [
        "67",
        "73"
      ],
      "x": "70",
      "masses": {
        "67": "1/2",
        "73": "1/2"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mean-outside-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/2; value 73 with probability 1/2. Sum masses for equal values. The candidate x is 71 units. Independently computed facts supplied for this question: exact weighted mean = 70; full set of modes = 67, 73; full support = 67, 73; probability of candidate x = 0. Statement: Under FI-5-mean-outside, the probability-weighted mean is 71 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/2; value 73 with probability 1/2. Sum masses for equal values. The candidate x is 71 units. Independently computed facts supplied for this question: exact weighted mean = 70; full set of modes = 67, 73; full support = 67, 73; probability of candidate x = 0. Statement: 71 units is mean-outcome(FI-5-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "batch size",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mean-outside-mean-outcome-False",
    "oracle": {
      "mean": "70",
      "modes": [
        "67",
        "73"
      ],
      "x": "71",
      "masses": {
        "67": "1/2",
        "73": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mean-outside-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/2; value 73 with probability 1/2. Sum masses for equal values. The candidate x is 73 units. Independently computed facts supplied for this question: exact weighted mean = 70; full set of modes = 67, 73; full support = 67, 73; probability of candidate x = 1/2. Statement: Under FI-5-mean-outside, 73 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/2; value 73 with probability 1/2. Sum masses for equal values. The candidate x is 73 units. Independently computed facts supplied for this question: exact weighted mean = 70; full set of modes = 67, 73; full support = 67, 73; probability of candidate x = 1/2. Statement: 73 units is likeliest-outcome(FI-5-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "batch size",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mean-outside-likeliest-outcome-True",
    "oracle": {
      "mean": "70",
      "modes": [
        "67",
        "73"
      ],
      "x": "73",
      "masses": {
        "67": "1/2",
        "73": "1/2"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mean-outside-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/2; value 73 with probability 1/2. Sum masses for equal values. The candidate x is 66 units. Independently computed facts supplied for this question: exact weighted mean = 70; full set of modes = 67, 73; full support = 67, 73; probability of candidate x = 0. Statement: Under FI-5-mean-outside, 66 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-outside, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/2; value 73 with probability 1/2. Sum masses for equal values. The candidate x is 66 units. Independently computed facts supplied for this question: exact weighted mean = 70; full set of modes = 67, 73; full support = 67, 73; probability of candidate x = 0. Statement: 66 units is likeliest-outcome(FI-5-mean-outside).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "batch size",
    "boundary": "mean-outside",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mean-outside-likeliest-outcome-False",
    "oracle": {
      "mean": "70",
      "modes": [
        "67",
        "73"
      ],
      "x": "66",
      "masses": {
        "67": "1/2",
        "73": "1/2"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mode-below-half-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 71 with probability 3/10; value 77 with probability 3/10. Sum masses for equal values. The candidate x is 356/5 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67; full support = 67, 71, 77; probability of candidate x = 0. Statement: Under FI-5-mode-below-half, the probability-weighted mean is 356/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 71 with probability 3/10; value 77 with probability 3/10. Sum masses for equal values. The candidate x is 356/5 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67; full support = 67, 71, 77; probability of candidate x = 0. Statement: 356/5 units is mean-outcome(FI-5-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "batch size",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mode-below-half-mean-outcome-True",
    "oracle": {
      "mean": "356/5",
      "modes": [
        "67"
      ],
      "x": "356/5",
      "masses": {
        "67": "2/5",
        "71": "3/10",
        "77": "3/10"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mode-below-half-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 71 with probability 3/10; value 77 with probability 3/10. Sum masses for equal values. The candidate x is 361/5 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67; full support = 67, 71, 77; probability of candidate x = 0. Statement: Under FI-5-mode-below-half, the probability-weighted mean is 361/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 71 with probability 3/10; value 77 with probability 3/10. Sum masses for equal values. The candidate x is 361/5 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67; full support = 67, 71, 77; probability of candidate x = 0. Statement: 361/5 units is mean-outcome(FI-5-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "batch size",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mode-below-half-mean-outcome-False",
    "oracle": {
      "mean": "356/5",
      "modes": [
        "67"
      ],
      "x": "361/5",
      "masses": {
        "67": "2/5",
        "71": "3/10",
        "77": "3/10"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mode-below-half-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 71 with probability 3/10; value 77 with probability 3/10. Sum masses for equal values. The candidate x is 67 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67; full support = 67, 71, 77; probability of candidate x = 2/5. Statement: Under FI-5-mode-below-half, 67 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 71 with probability 3/10; value 77 with probability 3/10. Sum masses for equal values. The candidate x is 67 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67; full support = 67, 71, 77; probability of candidate x = 2/5. Statement: 67 units is likeliest-outcome(FI-5-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "batch size",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mode-below-half-likeliest-outcome-True",
    "oracle": {
      "mean": "356/5",
      "modes": [
        "67"
      ],
      "x": "67",
      "masses": {
        "67": "2/5",
        "71": "3/10",
        "77": "3/10"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mode-below-half-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 71 with probability 3/10; value 77 with probability 3/10. Sum masses for equal values. The candidate x is 71 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67; full support = 67, 71, 77; probability of candidate x = 3/10. Statement: Under FI-5-mode-below-half, 71 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mode-below-half, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 71 with probability 3/10; value 77 with probability 3/10. Sum masses for equal values. The candidate x is 71 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67; full support = 67, 71, 77; probability of candidate x = 3/10. Statement: 71 units is likeliest-outcome(FI-5-mode-below-half).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "batch size",
    "boundary": "mode-below-half",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mode-below-half-likeliest-outcome-False",
    "oracle": {
      "mean": "356/5",
      "modes": [
        "67"
      ],
      "x": "71",
      "masses": {
        "67": "2/5",
        "71": "3/10",
        "77": "3/10"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-tied-modes-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 73 with probability 2/5; value 76 with probability 1/5. Sum masses for equal values. The candidate x is 356/5 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67, 73; full support = 67, 73, 76; probability of candidate x = 0. Statement: Under FI-5-tied-modes, the probability-weighted mean is 356/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 73 with probability 2/5; value 76 with probability 1/5. Sum masses for equal values. The candidate x is 356/5 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67, 73; full support = 67, 73, 76; probability of candidate x = 0. Statement: 356/5 units is mean-outcome(FI-5-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "batch size",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-tied-modes-mean-outcome-True",
    "oracle": {
      "mean": "356/5",
      "modes": [
        "67",
        "73"
      ],
      "x": "356/5",
      "masses": {
        "67": "2/5",
        "73": "2/5",
        "76": "1/5"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-tied-modes-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 73 with probability 2/5; value 76 with probability 1/5. Sum masses for equal values. The candidate x is 361/5 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67, 73; full support = 67, 73, 76; probability of candidate x = 0. Statement: Under FI-5-tied-modes, the probability-weighted mean is 361/5 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 73 with probability 2/5; value 76 with probability 1/5. Sum masses for equal values. The candidate x is 361/5 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67, 73; full support = 67, 73, 76; probability of candidate x = 0. Statement: 361/5 units is mean-outcome(FI-5-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "batch size",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-tied-modes-mean-outcome-False",
    "oracle": {
      "mean": "356/5",
      "modes": [
        "67",
        "73"
      ],
      "x": "361/5",
      "masses": {
        "67": "2/5",
        "73": "2/5",
        "76": "1/5"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-tied-modes-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 73 with probability 2/5; value 76 with probability 1/5. Sum masses for equal values. The candidate x is 73 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67, 73; full support = 67, 73, 76; probability of candidate x = 2/5. Statement: Under FI-5-tied-modes, 73 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 73 with probability 2/5; value 76 with probability 1/5. Sum masses for equal values. The candidate x is 73 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67, 73; full support = 67, 73, 76; probability of candidate x = 2/5. Statement: 73 units is likeliest-outcome(FI-5-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "batch size",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-tied-modes-likeliest-outcome-True",
    "oracle": {
      "mean": "356/5",
      "modes": [
        "67",
        "73"
      ],
      "x": "73",
      "masses": {
        "67": "2/5",
        "73": "2/5",
        "76": "1/5"
      },
      "flags": [
        true,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-tied-modes-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 73 with probability 2/5; value 76 with probability 1/5. Sum masses for equal values. The candidate x is 76 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67, 73; full support = 67, 73, 76; probability of candidate x = 1/5. Statement: Under FI-5-tied-modes, 76 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-tied-modes, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 2/5; value 73 with probability 2/5; value 76 with probability 1/5. Sum masses for equal values. The candidate x is 76 units. Independently computed facts supplied for this question: exact weighted mean = 356/5; full set of modes = 67, 73; full support = 67, 73, 76; probability of candidate x = 1/5. Statement: 76 units is likeliest-outcome(FI-5-tied-modes).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "batch size",
    "boundary": "tied-modes",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-tied-modes-likeliest-outcome-False",
    "oracle": {
      "mean": "356/5",
      "modes": [
        "67",
        "73"
      ],
      "x": "76",
      "masses": {
        "67": "2/5",
        "73": "2/5",
        "76": "1/5"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mean-is-mode-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/4; value 71 with probability 1/2; value 75 with probability 1/4. Sum masses for equal values. The candidate x is 71 units. Independently computed facts supplied for this question: exact weighted mean = 71; full set of modes = 71; full support = 67, 71, 75; probability of candidate x = 1/2. Statement: Under FI-5-mean-is-mode, the probability-weighted mean is 71 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/4; value 71 with probability 1/2; value 75 with probability 1/4. Sum masses for equal values. The candidate x is 71 units. Independently computed facts supplied for this question: exact weighted mean = 71; full set of modes = 71; full support = 67, 71, 75; probability of candidate x = 1/2. Statement: 71 units is mean-outcome(FI-5-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "batch size",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mean-is-mode-mean-outcome-True",
    "oracle": {
      "mean": "71",
      "modes": [
        "71"
      ],
      "x": "71",
      "masses": {
        "67": "1/4",
        "71": "1/2",
        "75": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mean-is-mode-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/4; value 71 with probability 1/2; value 75 with probability 1/4. Sum masses for equal values. The candidate x is 72 units. Independently computed facts supplied for this question: exact weighted mean = 71; full set of modes = 71; full support = 67, 71, 75; probability of candidate x = 0. Statement: Under FI-5-mean-is-mode, the probability-weighted mean is 72 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/4; value 71 with probability 1/2; value 75 with probability 1/4. Sum masses for equal values. The candidate x is 72 units. Independently computed facts supplied for this question: exact weighted mean = 71; full set of modes = 71; full support = 67, 71, 75; probability of candidate x = 0. Statement: 72 units is mean-outcome(FI-5-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "batch size",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mean-is-mode-mean-outcome-False",
    "oracle": {
      "mean": "71",
      "modes": [
        "71"
      ],
      "x": "72",
      "masses": {
        "67": "1/4",
        "71": "1/2",
        "75": "1/4"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mean-is-mode-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/4; value 71 with probability 1/2; value 75 with probability 1/4. Sum masses for equal values. The candidate x is 71 units. Independently computed facts supplied for this question: exact weighted mean = 71; full set of modes = 71; full support = 67, 71, 75; probability of candidate x = 1/2. Statement: Under FI-5-mean-is-mode, 71 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/4; value 71 with probability 1/2; value 75 with probability 1/4. Sum masses for equal values. The candidate x is 71 units. Independently computed facts supplied for this question: exact weighted mean = 71; full set of modes = 71; full support = 67, 71, 75; probability of candidate x = 1/2. Statement: 71 units is likeliest-outcome(FI-5-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "batch size",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mean-is-mode-likeliest-outcome-True",
    "oracle": {
      "mean": "71",
      "modes": [
        "71"
      ],
      "x": "71",
      "masses": {
        "67": "1/4",
        "71": "1/2",
        "75": "1/4"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-mean-is-mode-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/4; value 71 with probability 1/2; value 75 with probability 1/4. Sum masses for equal values. The candidate x is 67 units. Independently computed facts supplied for this question: exact weighted mean = 71; full set of modes = 71; full support = 67, 71, 75; probability of candidate x = 1/4. Statement: Under FI-5-mean-is-mode, 67 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-mean-is-mode, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 67 with probability 1/4; value 71 with probability 1/2; value 75 with probability 1/4. Sum masses for equal values. The candidate x is 67 units. Independently computed facts supplied for this question: exact weighted mean = 71; full set of modes = 71; full support = 67, 71, 75; probability of candidate x = 1/4. Statement: 67 units is likeliest-outcome(FI-5-mean-is-mode).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "batch size",
    "boundary": "mean-is-mode",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-mean-is-mode-likeliest-outcome-False",
    "oracle": {
      "mean": "71",
      "modes": [
        "71"
      ],
      "x": "67",
      "masses": {
        "67": "1/4",
        "71": "1/2",
        "75": "1/4"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-duplicate-paths-mean-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 68 with probability 1/4; value 68 with probability 1/4; value 74 with probability 1/3; value 77 with probability 1/6. Sum masses for equal values. The candidate x is 143/2 units. Independently computed facts supplied for this question: exact weighted mean = 143/2; full set of modes = 68; full support = 68, 74, 77; probability of candidate x = 0. Statement: Under FI-5-duplicate-paths, the probability-weighted mean is 143/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 68 with probability 1/4; value 68 with probability 1/4; value 74 with probability 1/3; value 77 with probability 1/6. Sum masses for equal values. The candidate x is 143/2 units. Independently computed facts supplied for this question: exact weighted mean = 143/2; full set of modes = 68; full support = 68, 74, 77; probability of candidate x = 0. Statement: 143/2 units is mean-outcome(FI-5-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "batch size",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-duplicate-paths-mean-outcome-True",
    "oracle": {
      "mean": "143/2",
      "modes": [
        "68"
      ],
      "x": "143/2",
      "masses": {
        "68": "1/2",
        "74": "1/3",
        "77": "1/6"
      },
      "flags": [
        true,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-duplicate-paths-mean-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 68 with probability 1/4; value 68 with probability 1/4; value 74 with probability 1/3; value 77 with probability 1/6. Sum masses for equal values. The candidate x is 145/2 units. Independently computed facts supplied for this question: exact weighted mean = 143/2; full set of modes = 68; full support = 68, 74, 77; probability of candidate x = 0. Statement: Under FI-5-duplicate-paths, the probability-weighted mean is 145/2 units.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 68 with probability 1/4; value 68 with probability 1/4; value 74 with probability 1/3; value 77 with probability 1/6. Sum masses for equal values. The candidate x is 145/2 units. Independently computed facts supplied for this question: exact weighted mean = 143/2; full set of modes = 68; full support = 68, 74, 77; probability of candidate x = 0. Statement: 145/2 units is mean-outcome(FI-5-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "mean-outcome",
    "form": "mean-outcome",
    "domain": "batch size",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-duplicate-paths-mean-outcome-False",
    "oracle": {
      "mean": "143/2",
      "modes": [
        "68"
      ],
      "x": "145/2",
      "masses": {
        "68": "1/2",
        "74": "1/3",
        "77": "1/6"
      },
      "flags": [
        false,
        false,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-duplicate-paths-likeliest-outcome-True",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 68 with probability 1/4; value 68 with probability 1/4; value 74 with probability 1/3; value 77 with probability 1/6. Sum masses for equal values. The candidate x is 68 units. Independently computed facts supplied for this question: exact weighted mean = 143/2; full set of modes = 68; full support = 68, 74, 77; probability of candidate x = 1/2. Statement: Under FI-5-duplicate-paths, 68 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 68 with probability 1/4; value 68 with probability 1/4; value 74 with probability 1/3; value 77 with probability 1/6. Sum masses for equal values. The candidate x is 68 units. Independently computed facts supplied for this question: exact weighted mean = 143/2; full set of modes = 68; full support = 68, 74, 77; probability of candidate x = 1/2. Statement: 68 units is likeliest-outcome(FI-5-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no."
    ],
    "answer": "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "batch size",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-duplicate-paths-likeliest-outcome-True",
    "oracle": {
      "mean": "143/2",
      "modes": [
        "68"
      ],
      "x": "68",
      "masses": {
        "68": "1/2",
        "74": "1/3",
        "77": "1/6"
      },
      "flags": [
        true,
        true,
        true,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-5-duplicate-paths-likeliest-outcome-False",
    "english": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 68 with probability 1/4; value 68 with probability 1/4; value 74 with probability 1/3; value 77 with probability 1/6. Sum masses for equal values. The candidate x is 74 units. Independently computed facts supplied for this question: exact weighted mean = 143/2; full set of modes = 68; full support = 68, 74, 77; probability of candidate x = 1/3. Statement: Under FI-5-duplicate-paths, 74 units has highest outcome probability, ties allowed.",
    "ainglish": "Shared definitions for this stateless question: mean-outcome(D) denotes the exact probability-weighted arithmetic mean; likeliest-outcome(D) denotes any value with maximal aggregated probability mass, with ties allowed. The same definitions govern the English expressions. Fictional batch size model FI-5-duplicate-paths, version v9, under its stated fixed conditioning, in units. Exact exhaustive mutually exclusive paths: value 68 with probability 1/4; value 68 with probability 1/4; value 74 with probability 1/3; value 77 with probability 1/6. Sum masses for equal values. The candidate x is 74 units. Independently computed facts supplied for this question: exact weighted mean = 143/2; full set of modes = 68; full support = 68, 74, 77; probability of candidate x = 1/3. Statement: 74 units is likeliest-outcome(FI-5-duplicate-paths).",
    "question": "Under the exact declared model D, evaluate statement truth, possibility of x, whether x is the unique mode, and whether a trial from D equals x with probability one.",
    "options": [
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: no; x possible: no; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: yes.",
      "Claim true: yes; x possible: no; x unique most probable: yes; next result guaranteed x under D: no.",
      "Claim true: yes; x possible: no; x unique most probable: no; next result guaranteed x under D: yes."
    ],
    "answer": "Claim true: no; x possible: yes; x unique most probable: no; next result guaranteed x under D: no.",
    "settlement_stratum": "likeliest-outcome",
    "form": "likeliest-outcome",
    "domain": "batch size",
    "boundary": "duplicate-paths",
    "supplied_facts": true,
    "response_format": "four-bit",
    "world_id": "5-duplicate-paths-likeliest-outcome-False",
    "oracle": {
      "mean": "143/2",
      "modes": [
        "68"
      ],
      "x": "74",
      "masses": {
        "68": "1/2",
        "74": "1/3",
        "77": "1/6"
      },
      "flags": [
        false,
        true,
        false,
        false
      ]
    }
  },
  {
    "id": "outcome-facts-four-bit-control-0",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7600: the custodian is not identified.",
    "ainglish": "Receipt FU-7600: the custodian is Iona.",
    "question": "Who holds the parcel on receipt FU-7600?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Iona"
  },
  {
    "id": "outcome-facts-four-bit-control-1",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7601: the custodian is not identified.",
    "ainglish": "Receipt FU-7601: the custodian is Juri.",
    "question": "Who holds the parcel on receipt FU-7601?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Juri"
  },
  {
    "id": "outcome-facts-four-bit-control-2",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7602: the custodian is not identified.",
    "ainglish": "Receipt FU-7602: the custodian is Kade.",
    "question": "Who holds the parcel on receipt FU-7602?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Kade"
  },
  {
    "id": "outcome-facts-four-bit-control-3",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7603: the custodian is not identified.",
    "ainglish": "Receipt FU-7603: the custodian is Lumi.",
    "question": "Who holds the parcel on receipt FU-7603?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Lumi"
  },
  {
    "id": "outcome-facts-four-bit-control-4",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7604: the custodian is not identified.",
    "ainglish": "Receipt FU-7604: the custodian is Iona.",
    "question": "Who holds the parcel on receipt FU-7604?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Iona"
  },
  {
    "id": "outcome-facts-four-bit-control-5",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7605: the custodian is not identified.",
    "ainglish": "Receipt FU-7605: the custodian is Juri.",
    "question": "Who holds the parcel on receipt FU-7605?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Juri"
  },
  {
    "id": "outcome-facts-four-bit-control-6",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7606: the custodian is not identified.",
    "ainglish": "Receipt FU-7606: the custodian is Kade.",
    "question": "Who holds the parcel on receipt FU-7606?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Kade"
  },
  {
    "id": "outcome-facts-four-bit-control-7",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7607: the custodian is not identified.",
    "ainglish": "Receipt FU-7607: the custodian is Lumi.",
    "question": "Who holds the parcel on receipt FU-7607?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Lumi"
  },
  {
    "id": "outcome-facts-four-bit-control-8",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7608: the custodian is not identified.",
    "ainglish": "Receipt FU-7608: the custodian is Iona.",
    "question": "Who holds the parcel on receipt FU-7608?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Iona"
  },
  {
    "id": "outcome-facts-four-bit-control-9",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7609: the custodian is not identified.",
    "ainglish": "Receipt FU-7609: the custodian is Juri.",
    "question": "Who holds the parcel on receipt FU-7609?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Juri"
  },
  {
    "id": "outcome-facts-four-bit-control-10",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7610: the custodian is not identified.",
    "ainglish": "Receipt FU-7610: the custodian is Kade.",
    "question": "Who holds the parcel on receipt FU-7610?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Kade"
  },
  {
    "id": "outcome-facts-four-bit-control-11",
    "calibration": true,
    "calibration_scope": "target-independent",
    "calibration_construct": "resolved custody",
    "english": "Receipt FU-7611: the custodian is not identified.",
    "ainglish": "Receipt FU-7611: the custodian is Lumi.",
    "question": "Who holds the parcel on receipt FU-7611?",
    "options": [
      "Iona",
      "Juri",
      "Kade",
      "Lumi",
      "not determined"
    ],
    "answer": "Lumi"
  }
]