{
 "n": 227,
 "domains": {
  "Algebra": 97,
  "Complex Analysis": 19,
  "Real Analysis": 48,
  "Topology": 63
 },
 "one_shot": {
  "Kimina Prover": {
   "n": 217,
   "compile": 24,
   "faithful": 10,
   "compile_pct": 11.1,
   "faithful_pct": 4.6,
   "gap_pts": 6.5,
   "gpt_pos": 10,
   "gem_pos": 12,
   "consensus": 10,
   "gpt_only": 0
  },
  "Goedel Prover": {
   "n": 227,
   "compile": 47,
   "faithful": 14,
   "compile_pct": 20.7,
   "faithful_pct": 6.2,
   "gap_pts": 14.5,
   "gpt_pos": 15,
   "gem_pos": 15,
   "consensus": 14,
   "gpt_only": 1
  },
  "Kimina AutoF": {
   "n": 217,
   "compile": 73,
   "faithful": 27,
   "compile_pct": 33.6,
   "faithful_pct": 12.4,
   "gap_pts": 21.2,
   "gpt_pos": 27,
   "gem_pos": 32,
   "consensus": 27,
   "gpt_only": 0
  },
  "Herald": {
   "n": 227,
   "compile": 49,
   "faithful": 23,
   "compile_pct": 21.6,
   "faithful_pct": 10.1,
   "gap_pts": 11.5,
   "gpt_pos": 23,
   "gem_pos": 27,
   "consensus": 23,
   "gpt_only": 0
  },
  "StepFun": {
   "n": 217,
   "compile": 44,
   "faithful": 30,
   "compile_pct": 20.3,
   "faithful_pct": 13.8,
   "gap_pts": 6.5,
   "gpt_pos": 30,
   "gem_pos": 35,
   "consensus": 30,
   "gpt_only": 0
  },
  "GPT-5.2": {
   "n": 227,
   "compile": 54,
   "faithful": 45,
   "compile_pct": 23.8,
   "faithful_pct": 19.8,
   "gap_pts": 4.0,
   "gpt_pos": 47,
   "gem_pos": 48,
   "consensus": 45,
   "gpt_only": 2
  },
  "Gemini-2.5-Pro": {
   "n": 227,
   "compile": 65,
   "faithful": 62,
   "compile_pct": 28.6,
   "faithful_pct": 27.3,
   "gap_pts": 1.3,
   "gpt_pos": 62,
   "gem_pos": 65,
   "consensus": 62,
   "gpt_only": 0
  },
  "Sonnet 4.5": {
   "n": 227,
   "compile": 96,
   "faithful": 74,
   "compile_pct": 42.3,
   "faithful_pct": 32.6,
   "gap_pts": 9.7,
   "gpt_pos": 74,
   "gem_pos": 88,
   "consensus": 74,
   "gpt_only": 0
  }
 },
 "configs": {
  "000": {
   "n": 227,
   "compile": 54,
   "faithful": 45,
   "compile_pct": 23.8,
   "faithful_pct": 19.8,
   "gap_pts": 4.0,
   "gpt_pos": 47,
   "gem_pos": 48,
   "consensus": 45,
   "gpt_only": 2
  },
  "001": {
   "n": 227,
   "compile": 109,
   "faithful": 80,
   "compile_pct": 48.0,
   "faithful_pct": 35.2,
   "gap_pts": 12.8,
   "gpt_pos": 81,
   "gem_pos": 94,
   "consensus": 80,
   "gpt_only": 1
  },
  "010": {
   "n": 227,
   "compile": 203,
   "faithful": 127,
   "compile_pct": 89.4,
   "faithful_pct": 55.9,
   "gap_pts": 33.5,
   "gpt_pos": 130,
   "gem_pos": 163,
   "consensus": 127,
   "gpt_only": 3
  },
  "011": {
   "n": 227,
   "compile": 189,
   "faithful": 132,
   "compile_pct": 83.3,
   "faithful_pct": 58.1,
   "gap_pts": 25.1,
   "gpt_pos": 133,
   "gem_pos": 157,
   "consensus": 132,
   "gpt_only": 1
  },
  "100": {
   "n": 227,
   "compile": 65,
   "faithful": 56,
   "compile_pct": 28.6,
   "faithful_pct": 24.7,
   "gap_pts": 4.0,
   "gpt_pos": 56,
   "gem_pos": 62,
   "consensus": 56,
   "gpt_only": 0
  },
  "101": {
   "n": 227,
   "compile": 121,
   "faithful": 84,
   "compile_pct": 53.3,
   "faithful_pct": 37.0,
   "gap_pts": 16.3,
   "gpt_pos": 85,
   "gem_pos": 106,
   "consensus": 84,
   "gpt_only": 1
  },
  "110": {
   "n": 227,
   "compile": 207,
   "faithful": 122,
   "compile_pct": 91.2,
   "faithful_pct": 53.7,
   "gap_pts": 37.4,
   "gpt_pos": 124,
   "gem_pos": 154,
   "consensus": 122,
   "gpt_only": 2
  },
  "111": {
   "n": 227,
   "compile": 198,
   "faithful": 131,
   "compile_pct": 87.2,
   "faithful_pct": 57.7,
   "gap_pts": 29.5,
   "gpt_pos": 134,
   "gem_pos": 158,
   "consensus": 131,
   "gpt_only": 3
  }
 },
 "alt_orchestrators": {
  "Sonnet 4.5": {
   "n": 227,
   "compile": 206,
   "faithful": 145,
   "compile_pct": 90.7,
   "faithful_pct": 63.9,
   "gap_pts": 26.9,
   "gpt_pos": 148,
   "gem_pos": 175,
   "consensus": 145,
   "gpt_only": 3
  },
  "Gemini-2.5-Pro": {
   "n": 227,
   "compile": 172,
   "faithful": 147,
   "compile_pct": 75.8,
   "faithful_pct": 64.8,
   "gap_pts": 11.0,
   "gpt_pos": 147,
   "gem_pos": 167,
   "consensus": 147,
   "gpt_only": 0
  }
 },
 "figure1": {
  "Kimina Prover": {
   "n": 217,
   "compile": 24,
   "faithful": 10,
   "compile_pct": 11.1,
   "faithful_pct": 4.6,
   "gap_pts": 6.5,
   "gpt_pos": 10,
   "gem_pos": 12,
   "consensus": 10,
   "gpt_only": 0
  },
  "Goedel Prover": {
   "n": 227,
   "compile": 47,
   "faithful": 14,
   "compile_pct": 20.7,
   "faithful_pct": 6.2,
   "gap_pts": 14.5,
   "gpt_pos": 15,
   "gem_pos": 15,
   "consensus": 14,
   "gpt_only": 1
  },
  "Kimina AutoF": {
   "n": 217,
   "compile": 73,
   "faithful": 27,
   "compile_pct": 33.6,
   "faithful_pct": 12.4,
   "gap_pts": 21.2,
   "gpt_pos": 27,
   "gem_pos": 32,
   "consensus": 27,
   "gpt_only": 0
  },
  "Herald": {
   "n": 227,
   "compile": 49,
   "faithful": 23,
   "compile_pct": 21.6,
   "faithful_pct": 10.1,
   "gap_pts": 11.5,
   "gpt_pos": 23,
   "gem_pos": 27,
   "consensus": 23,
   "gpt_only": 0
  },
  "StepFun": {
   "n": 217,
   "compile": 44,
   "faithful": 30,
   "compile_pct": 20.3,
   "faithful_pct": 13.8,
   "gap_pts": 6.5,
   "gpt_pos": 30,
   "gem_pos": 35,
   "consensus": 30,
   "gpt_only": 0
  },
  "GPT-5.2": {
   "n": 227,
   "compile": 54,
   "faithful": 45,
   "compile_pct": 23.8,
   "faithful_pct": 19.8,
   "gap_pts": 4.0,
   "gpt_pos": 47,
   "gem_pos": 48,
   "consensus": 45,
   "gpt_only": 2
  },
  "Gemini-2.5-Pro": {
   "n": 227,
   "compile": 65,
   "faithful": 62,
   "compile_pct": 28.6,
   "faithful_pct": 27.3,
   "gap_pts": 1.3,
   "gpt_pos": 62,
   "gem_pos": 65,
   "consensus": 62,
   "gpt_only": 0
  },
  "GPT-5.2 agent": {
   "n": 227,
   "compile": 198,
   "faithful": 131,
   "compile_pct": 87.2,
   "faithful_pct": 57.7,
   "gap_pts": 29.5,
   "gpt_pos": 134,
   "gem_pos": 158,
   "consensus": 131,
   "gpt_only": 3
  }
 },
 "factorial": {
  "configs": {
   "000": {
    "compile": 54,
    "faithful": 45,
    "compile_pct": 23.8,
    "faithful_pct": 19.8,
    "faithful_given_compile_pct": 83.3,
    "gap_count": 9
   },
   "001": {
    "compile": 109,
    "faithful": 80,
    "compile_pct": 48.0,
    "faithful_pct": 35.2,
    "faithful_given_compile_pct": 73.4,
    "gap_count": 29
   },
   "010": {
    "compile": 203,
    "faithful": 127,
    "compile_pct": 89.4,
    "faithful_pct": 55.9,
    "faithful_given_compile_pct": 62.6,
    "gap_count": 76
   },
   "011": {
    "compile": 189,
    "faithful": 132,
    "compile_pct": 83.3,
    "faithful_pct": 58.1,
    "faithful_given_compile_pct": 69.8,
    "gap_count": 57
   },
   "100": {
    "compile": 65,
    "faithful": 56,
    "compile_pct": 28.6,
    "faithful_pct": 24.7,
    "faithful_given_compile_pct": 86.2,
    "gap_count": 9
   },
   "101": {
    "compile": 121,
    "faithful": 84,
    "compile_pct": 53.3,
    "faithful_pct": 37.0,
    "faithful_given_compile_pct": 69.4,
    "gap_count": 37
   },
   "110": {
    "compile": 207,
    "faithful": 122,
    "compile_pct": 91.2,
    "faithful_pct": 53.7,
    "faithful_given_compile_pct": 58.9,
    "gap_count": 85
   },
   "111": {
    "compile": 198,
    "faithful": 131,
    "compile_pct": 87.2,
    "faithful_pct": 57.7,
    "faithful_given_compile_pct": 66.2,
    "gap_count": 67
   }
  },
  "effects_faithful": {
   "T": {
    "effect": 1.0,
    "ci95": [
     -1.7,
     3.9
    ]
   },
   "F": {
    "effect": 27.2,
    "ci95": [
     22.6,
     31.7
    ]
   },
   "S": {
    "effect": 8.5,
    "ci95": [
     5.4,
     11.6
    ]
   },
   "FxS": {
    "effect": -10.8,
    "ci95": [
     -17.2,
     -4.4
    ]
   },
   "FxT": {
    "effect": -4.6,
    "ci95": [
     -10.1,
     0.9
    ]
   },
   "SxT": {
    "effect": -0.7,
    "ci95": [
     -6.2,
     4.8
    ]
   }
  },
  "effects_all": {
   "T": {
    "faithful": {
     "effect": 1.0,
     "ci95": [
      -1.9,
      3.7
     ]
    },
    "compile": {
     "effect": 4.0,
     "ci95": [
      1.3,
      6.6
     ]
    },
    "gap": {
     "effect": 3.0,
     "ci95": [
      0.2,
      5.7
     ]
    }
   },
   "F": {
    "faithful": {
     "effect": 27.2,
     "ci95": [
      22.7,
      31.8
     ]
    },
    "compile": {
     "effect": 49.3,
     "ci95": [
      44.5,
      54.0
     ]
    },
    "gap": {
     "effect": 22.1,
     "ci95": [
      18.0,
      26.3
     ]
    }
   },
   "S": {
    "faithful": {
     "effect": 8.5,
     "ci95": [
      5.4,
      11.6
     ]
    },
    "compile": {
     "effect": 9.7,
     "ci95": [
      6.7,
      12.7
     ]
    },
    "gap": {
     "effect": 1.2,
     "ci95": [
      -1.8,
      4.3
     ]
    }
   }
  },
  "conditional_all": {
   "S|F=0": {
    "faithful": {
     "effect": 13.9,
     "ci95": [
      9.3,
      18.3
     ]
    },
    "compile": {
     "effect": 24.4,
     "ci95": [
      19.6,
      29.3
     ]
    },
    "gap": {
     "effect": 10.6,
     "ci95": [
      7.0,
      14.3
     ]
    }
   },
   "S|F=1": {
    "faithful": {
     "effect": 3.1,
     "ci95": [
      -1.3,
      7.7
     ]
    },
    "compile": {
     "effect": -5.1,
     "ci95": [
      -8.6,
      -1.8
     ]
    },
    "gap": {
     "effect": -8.1,
     "ci95": [
      -12.8,
      -3.5
     ]
    }
   },
   "T|F=0": {
    "faithful": {
     "effect": 3.3,
     "ci95": [
      -0.2,
      7.0
     ]
    },
    "compile": {
     "effect": 5.1,
     "ci95": [
      0.9,
      9.3
     ]
    },
    "gap": {
     "effect": 1.8,
     "ci95": [
      -1.3,
      4.8
     ]
    }
   },
   "T|F=1": {
    "faithful": {
     "effect": -1.3,
     "ci95": [
      -5.5,
      2.9
     ]
    },
    "compile": {
     "effect": 2.9,
     "ci95": [
      -0.7,
      6.4
     ]
    },
    "gap": {
     "effect": 4.2,
     "ci95": [
      -0.7,
      8.8
     ]
    }
   },
   "F|S=0": {
    "faithful": {
     "effect": 32.6,
     "ci95": [
      26.7,
      38.3
     ]
    },
    "compile": {
     "effect": 64.1,
     "ci95": [
      58.6,
      69.4
     ]
    },
    "gap": {
     "effect": 31.5,
     "ci95": [
      26.2,
      36.8
     ]
    }
   },
   "F|S=1": {
    "faithful": {
     "effect": 21.8,
     "ci95": [
      16.5,
      27.3
     ]
    },
    "compile": {
     "effect": 34.6,
     "ci95": [
      28.9,
      40.3
     ]
    },
    "gap": {
     "effect": 12.8,
     "ci95": [
      7.9,
      17.6
     ]
    }
   }
  },
  "threshold": {
   "7": {
    "effects": {
     "T": 2.1,
     "F": 30.9,
     "S": 8.3
    },
    "gap_111_pts": 24.7
   },
   "8": {
    "effects": {
     "T": 1.2,
     "F": 29.2,
     "S": 8.5
    },
    "gap_111_pts": 26.4
   },
   "9": {
    "effects": {
     "T": 1.0,
     "F": 27.2,
     "S": 8.5
    },
    "gap_111_pts": 29.5
   },
   "10": {
    "effects": {
     "T": 1.0,
     "F": 21.7,
     "S": 6.9
    },
    "gap_111_pts": 37.9
   }
  },
  "transition_ledger": {
   "000->010": {
    "new": 90,
    "lost": 8,
    "net": 82
   },
   "001->011": {
    "new": 59,
    "lost": 7,
    "net": 52
   },
   "101->111": {
    "new": 62,
    "lost": 15,
    "net": 47
   },
   "010->011": {
    "new": 30,
    "lost": 25,
    "net": 5
   },
   "110->111": {
    "new": 26,
    "lost": 17,
    "net": 9
   },
   "011->111": {
    "new": 23,
    "lost": 24,
    "net": -1
   }
  },
  "oracle": {
   "faithful_111": 131,
   "any": 175,
   "all": 27,
   "never": 52,
   "missed_by_111_faithful_elsewhere": 44,
   "missed_compile_pass_111": 34
  }
 },
 "trajectory": {
  "F1": {
   "1-2": {
    "faithful": 165,
    "n": 199
   },
   "3-5": {
    "faithful": 136,
    "n": 199
   },
   "6-9": {
    "faithful": 113,
    "n": 180
   },
   "10-12": {
    "faithful": 46,
    "n": 92
   },
   "13-18": {
    "faithful": 34,
    "n": 81
   },
   "19-24": {
    "faithful": 18,
    "n": 157
   }
  },
  "F0": {
   "1-2": {
    "faithful": 67,
    "n": 194
   },
   "3-5": {
    "faithful": 72,
    "n": 187
   },
   "6-9": {
    "faithful": 32,
    "n": 110
   },
   "10-12": {
    "faithful": 14,
    "n": 43
   },
   "13-18": {
    "faithful": 21,
    "n": 73
   },
   "19-24": {
    "faithful": 14,
    "n": 74
   }
  }
 },
 "tool_usage": {
  "010": {
   "translator": 0,
   "repl": 899,
   "search_total": 0
  },
  "011": {
   "translator": 0,
   "repl": 641,
   "search_total": 1157
  },
  "110": {
   "translator": 148,
   "repl": 864,
   "search_total": 0
  },
  "111": {
   "translator": 48,
   "repl": 586,
   "search_total": 1274
  }
 },
 "third_judge": {
  "all_8": {
   "coverage": {
    "k": 1123,
    "n": 1146,
    "pct": 98.0,
    "wilson95": [
     97.0,
     98.7
    ]
   },
   "agreement": {
    "k": 981,
    "n": 1123,
    "pct": 87.4,
    "wilson95": [
     85.3,
     89.2
    ]
   },
   "positive_confirmed": {
    "k": 712,
    "n": 774,
    "pct": 92.0,
    "wilson95": [
     89.9,
     93.7
    ]
   },
   "negative_confirmed": {
    "k": 269,
    "n": 349,
    "pct": 77.1,
    "wilson95": [
     72.4,
     81.2
    ]
   }
  },
  "config_111": {
   "coverage": {
    "k": 195,
    "n": 198,
    "pct": 98.5,
    "wilson95": [
     95.6,
     99.5
    ]
   },
   "agreement": {
    "k": 174,
    "n": 195,
    "pct": 89.2,
    "wilson95": [
     84.1,
     92.8
    ]
   },
   "positive_confirmed": {
    "k": 120,
    "n": 131,
    "pct": 91.6,
    "wilson95": [
     85.6,
     95.2
    ]
   },
   "negative_confirmed": {
    "k": 54,
    "n": 64,
    "pct": 84.4,
    "wilson95": [
     73.6,
     91.3
    ]
   }
  }
 },
 "human": {
  "reviewer1": {
   "scored": 72,
   "strict_positive": 70,
   "precision_strict": {
    "k": 67,
    "n": 70,
    "pct": 95.7,
    "wilson95": [
     88.1,
     98.5
    ]
   }
  },
  "batch_A": {
   "selected": 67,
   "confirmed_negative": {
    "k": 54,
    "n": 67,
    "pct": 80.6,
    "wilson95": [
     69.6,
     88.3
    ]
   }
  },
  "batch_B": {
   "statements": 60,
   "effective": 59,
   "agreement": {
    "k": 54,
    "n": 59,
    "pct": 91.5,
    "wilson95": [
     81.6,
     96.3
    ]
   },
   "precision": {
    "k": 44,
    "n": 46,
    "pct": 95.7,
    "wilson95": [
     85.5,
     98.8
    ]
   },
   "compile_pass_negative_confirmed": {
    "k": 4,
    "n": 7,
    "pct": 57.1,
    "wilson95": [
     25.0,
     84.2
    ]
   },
   "all_negative_confirmed": {
    "k": 10,
    "n": 13,
    "pct": 76.9,
    "wilson95": [
     49.7,
     91.8
    ]
   }
  },
  "leanscorer": {
   "agreement_leanscorer": {
    "k": 45,
    "n": 59,
    "pct": 76.3,
    "wilson95": [
     64.0,
     85.3
    ]
   },
   "paired": {
    "both": 43,
    "ours_only": 11,
    "leanscorer_only": 2
   },
   "mcnemar_exact_p": 0.0225
  }
 },
 "beq": {
  "anchors": 40,
  "pairs": 183,
  "certified": 113,
  "dropped_anchor_ids": [
   "BC188",
   "BC224"
  ],
  "different_encoding": {
   "certified": 67,
   "n": 137
  },
  "certified_exact": 105,
  "anchor_bootstrap_ci95": [
   48.9,
   73.3
  ],
  "same_encoding": {
   "certified": 46,
   "n": 46
  }
 },
 "domain": {
  "Algebra": {
   "n": 97,
   "feedback": {
    "d_compile": 45.4,
    "d_faithful": 21.4,
    "d_gap": 24.0,
    "faithful_given_compile_F1_pct": 64.0
   },
   "faithful_rate_by_config": {
    "000": 0.278,
    "001": 0.412,
    "010": 0.546,
    "011": 0.577,
    "100": 0.278,
    "101": 0.433,
    "110": 0.567,
    "111": 0.567
   }
  },
  "Complex Analysis": {
   "n": 19,
   "feedback": {
    "d_compile": 64.5,
    "d_faithful": 47.4,
    "d_gap": 17.1,
    "faithful_given_compile_F1_pct": 76.7
   },
   "faithful_rate_by_config": {
    "000": 0.053,
    "001": 0.368,
    "010": 0.842,
    "011": 0.737,
    "100": 0.263,
    "101": 0.368,
    "110": 0.684,
    "111": 0.684
   }
  },
  "Real Analysis": {
   "n": 48,
   "feedback": {
    "d_compile": 62.0,
    "d_faithful": 35.9,
    "d_gap": 26.0,
    "faithful_given_compile_F1_pct": 58.7
   },
   "faithful_rate_by_config": {
    "000": 0.083,
    "001": 0.229,
    "010": 0.521,
    "011": 0.542,
    "100": 0.146,
    "101": 0.208,
    "110": 0.479,
    "111": 0.562
   }
  },
  "Topology": {
   "n": 63,
   "feedback": {
    "d_compile": 41.3,
    "d_faithful": 23.4,
    "d_gap": 17.9,
    "faithful_given_compile_F1_pct": 64.8
   },
   "faithful_rate_by_config": {
    "000": 0.206,
    "001": 0.349,
    "010": 0.524,
    "011": 0.571,
    "100": 0.27,
    "101": 0.397,
    "110": 0.492,
    "111": 0.571
   }
  }
 },
 "judge_disagreement_by_domain": {
  "Algebra": 79,
  "Complex Analysis": 16,
  "Topology": 34,
  "Real Analysis": 56
 },
 "newer_models": {
  "GPT-5.2": {
   "n": 227,
   "compile": 54,
   "accepted": 47,
   "compile_pct": 23.8,
   "accepted_pct": 20.7,
   "gap_pts": 3.1
  },
  "Gemini-2.5-Pro": {
   "n": 227,
   "compile": 65,
   "accepted": 62,
   "compile_pct": 28.6,
   "accepted_pct": 27.3,
   "gap_pts": 1.3
  },
  "Sonnet 4.5": {
   "n": 227,
   "compile": 96,
   "accepted": 74,
   "compile_pct": 42.3,
   "accepted_pct": 32.6,
   "gap_pts": 9.7
  },
  "GPT-5.2 agent": {
   "n": 227,
   "compile": 198,
   "accepted": 134,
   "compile_pct": 87.2,
   "accepted_pct": 59.0,
   "gap_pts": 28.2,
   "human_audit": {
    "rejected": 64,
    "translation_errors": 53,
    "translation_errors_pts": 23.3
   }
  },
  "GPT-6 Astra": {
   "n": 227,
   "compile": 214,
   "accepted": 189,
   "compile_pct": 94.3,
   "accepted_pct": 83.3,
   "gap_pts": 11.0,
   "review": {
    "rejected": 25,
    "final": {
     "J": 16,
     "B": 4,
     "T": 1,
     "J/B": 4
    },
    "translation_errors": 1,
    "translation_errors_pts": 0.4
   }
  },
  "Claude Opus 5.5": {
   "n": 227,
   "compile": 218,
   "accepted": 189,
   "compile_pct": 96.0,
   "accepted_pct": 83.3,
   "gap_pts": 12.8,
   "review": {
    "rejected": 29,
    "final": {
     "T": 3,
     "J": 16,
     "B": 7,
     "J/B": 3
    },
    "translation_errors": 3,
    "translation_errors_pts": 1.3
   }
  },
  "judge_failures": {
   "encoding": 20,
   "defective_item": 11,
   "identical": 10,
   "wrong_reason": 9
  },
  "sonnet5_on_judge_failures": {
   "graded": 49,
   "also_rejects": 29
  },
  "false_rejection_rate": {
   "Aristotle": {
    "rule": "compiles and GPT-5.2 >= 9",
    "rejected_faithful": 1,
    "faithful": 47,
    "pct": 2.1,
    "unfaithful_share": 0.1132,
    "real_error_share_of_rejections": 0.8
   },
   "GPT-5.2 agent": {
    "rule": "compiles and GPT-5.2 >= 9",
    "rejected_faithful": 11,
    "rejected": 64,
    "audit_precision": 0.957,
    "pct_estimated": 7.9,
    "unfaithful_share": 0.3011,
    "real_error_share_of_rejections": 0.8281
   },
   "GPT-6 Astra": {
    "rule": "compiles and GPT-5.2 >= 9",
    "rejected_not_at_fault": 24,
    "accepted": 189,
    "pct": 11.3,
    "pct_judged_faithful_only": 7.8,
    "unfaithful_share": 0.0047,
    "real_error_share_of_rejections": 0.04
   },
   "Claude Opus 5.5": {
    "rule": "compiles and GPT-5.2 >= 9",
    "rejected_not_at_fault": 26,
    "accepted": 189,
    "pct": 12.1,
    "pct_judged_faithful_only": 7.8,
    "unfaithful_share": 0.0138,
    "real_error_share_of_rejections": 0.1034
   }
  },
  "sensitivity_without_flagged": {
   "flagged": 18,
   "statements": 209,
   "criterion": {
    "Kimina Prover": {
     "n": 200,
     "compile": 24,
     "faithful": 10,
     "compile_pct": 12.0,
     "faithful_pct": 5.0,
     "gap_pts": 7.0,
     "gpt_pos": 10,
     "gem_pos": 12,
     "consensus": 10,
     "gpt_only": 0
    },
    "Goedel Prover": {
     "n": 209,
     "compile": 44,
     "faithful": 14,
     "compile_pct": 21.1,
     "faithful_pct": 6.7,
     "gap_pts": 14.4,
     "gpt_pos": 15,
     "gem_pos": 15,
     "consensus": 14,
     "gpt_only": 1
    },
    "Kimina AutoF": {
     "n": 200,
     "compile": 69,
     "faithful": 26,
     "compile_pct": 34.5,
     "faithful_pct": 13.0,
     "gap_pts": 21.5,
     "gpt_pos": 26,
     "gem_pos": 31,
     "consensus": 26,
     "gpt_only": 0
    },
    "Herald": {
     "n": 209,
     "compile": 46,
     "faithful": 22,
     "compile_pct": 22.0,
     "faithful_pct": 10.5,
     "gap_pts": 11.5,
     "gpt_pos": 22,
     "gem_pos": 25,
     "consensus": 22,
     "gpt_only": 0
    },
    "StepFun": {
     "n": 200,
     "compile": 39,
     "faithful": 28,
     "compile_pct": 19.5,
     "faithful_pct": 14.0,
     "gap_pts": 5.5,
     "gpt_pos": 28,
     "gem_pos": 32,
     "consensus": 28,
     "gpt_only": 0
    },
    "GPT-5.2": {
     "n": 209,
     "compile": 49,
     "faithful": 42,
     "compile_pct": 23.4,
     "faithful_pct": 20.1,
     "gap_pts": 3.3,
     "gpt_pos": 43,
     "gem_pos": 45,
     "consensus": 42,
     "gpt_only": 1
    },
    "Gemini-2.5-Pro": {
     "n": 209,
     "compile": 61,
     "faithful": 58,
     "compile_pct": 29.2,
     "faithful_pct": 27.8,
     "gap_pts": 1.4,
     "gpt_pos": 58,
     "gem_pos": 61,
     "consensus": 58,
     "gpt_only": 0
    },
    "Sonnet 4.5": {
     "n": 209,
     "compile": 88,
     "faithful": 70,
     "compile_pct": 42.1,
     "faithful_pct": 33.5,
     "gap_pts": 8.6,
     "gpt_pos": 70,
     "gem_pos": 81,
     "consensus": 70,
     "gpt_only": 0
    },
    "GPT-5.2 agent": {
     "n": 209,
     "compile": 182,
     "faithful": 124,
     "compile_pct": 87.1,
     "faithful_pct": 59.3,
     "gap_pts": 27.8,
     "gpt_pos": 127,
     "gem_pos": 147,
     "consensus": 124,
     "gpt_only": 3
    }
   },
   "gpt_only": {
    "GPT-5.2 agent": {
     "n": 209,
     "compile": 182,
     "accepted": 127,
     "compile_pct": 87.1,
     "accepted_pct": 60.8,
     "gap_pts": 26.3,
     "human_audit": {
      "rejected": 55,
      "translation_errors": 45,
      "translation_errors_pts": 21.5
     }
    },
    "GPT-6 Astra": {
     "n": 209,
     "compile": 197,
     "accepted": 182,
     "compile_pct": 94.3,
     "accepted_pct": 87.1,
     "gap_pts": 7.2,
     "review": {
      "rejected": 15,
      "final": {
       "J": 14,
       "T": 1
      },
      "either_review_T": 2
     }
    },
    "Claude Opus 5.5": {
     "n": 209,
     "compile": 204,
     "accepted": 184,
     "compile_pct": 97.6,
     "accepted_pct": 88.0,
     "gap_pts": 9.6,
     "review": {
      "rejected": 20,
      "final": {
       "T": 3,
       "J": 14,
       "B": 1,
       "J/B": 2
      },
      "either_review_T": 4
     }
    }
   }
  },
  "reviewer_validation": {
   "n": 74,
   "agreement": {
    "k": 58,
    "n": 74,
    "pct": 78.4,
    "wilson95": [
     67.7,
     86.2
    ]
   },
   "unfaithful_classified_T": {
    "k": 47,
    "n": 58,
    "pct": 81.0,
    "wilson95": [
     69.1,
     89.1
    ]
   },
   "faithful_classified_not_T": {
    "k": 11,
    "n": 16,
    "pct": 68.8,
    "wilson95": [
     44.4,
     85.8
    ]
   },
   "classes_unfaithful": {
    "T": 47,
    "J": 6,
    "B": 5
   },
   "classes_faithful": {
    "B": 5,
    "T": 5,
    "J": 6
   }
  },
  "regrade": {
   "rejected_not_errors": {
    "n": 50,
    "majority_accepts": 13,
    "at_least_one_accepts": 24,
    "at_least_one_rejects": 48
   },
   "rejected_errors": {
    "n": 4,
    "majority_accepts": 2,
    "at_least_one_accepts": 3,
    "at_least_one_rejects": 4
   },
   "accepted_sample": {
    "n": 40,
    "majority_accepts": 36,
    "at_least_one_accepts": 39,
    "at_least_one_rejects": 7
   }
  }
 }
}