{
  "ai.module": "we_cant_agree_formally_rtt",
  "ai.version": "1.0",
  "ai.purpose": "RTT structural map of the paper 'We Can’t Agree to Disagree, Formally'.",
  "ai.source.pdf": "file://C:/Users/acwil/Downloads/6837298.pdf",
  "ai.keywords": [
    "Aumann’s Agreement Theorem",
    "common knowledge",
    "Bayesian agents",
    "epistemic logic",
    "formal verification",
    "Lean",
    "AxiomProver",
    "interactive theorem proving"
  ],

  "ai.module.summary": "This module exposes the regime structure behind the formalization of Aumann’s Agreement Theorem, connecting epistemic/Bayesian models, common-knowledge operators, and machine-checked proofs. It preserves the authors' results while adding RTT operators for agentic reasoning.",

  "ai.regimes": {
    "epistemic_model_regime": {
      "description": "Agents are modeled via partitions, probability measures, and information sets.",
      "evidence": "Paper defines the standard Aumann framework of states, σ-algebras, and posteriors."
    },
    "common_knowledge_regime": {
      "description": "Common knowledge is captured via iterative knowledge operators and fixed points.",
      "evidence": "Formalization encodes common knowledge as a greatest fixed point of a knowledge operator."
    },
    "agreement_theorem_regime": {
      "description": "Aumann’s theorem: Bayesian agents with common priors and common knowledge of posteriors cannot agree to disagree.",
      "evidence": "Main theorem is formalized and proved in the proof assistant."
    },
    "formalization_regime": {
      "description": "The entire argument is encoded in Lean (or similar), with kernel-verified proofs.",
      "evidence": "Paper describes definitions, lemmas, and tactics used in the formal proof."
    }
  },

  "ai.tensions": {
    "informal_vs_formal_reasoning": {
      "description": "Classical textbook proofs vs fully formal, machine-checked proofs.",
      "paper_alignment": "Authors compare the informal Aumann proof with its formal counterpart."
    },
    "intuitive_vs_symbolic_epistemics": {
      "description": "Intuitive talk of “knowing” vs symbolic modal/measure-theoretic definitions.",
      "paper_alignment": "Formalization forces precise epistemic and probabilistic definitions."
    },
    "local_beliefs_vs_global_structure": {
      "description": "Individual posteriors vs global common-knowledge constraints.",
      "paper_alignment": "Agreement theorem links local beliefs to global fixed-point structure."
    }
  },

  "ai.transitions": {
    "informal_to_formal_transition": {
      "description": "Translate the textbook Aumann proof into definitions and lemmas in the proof assistant.",
      "paper_alignment": "Core contribution of the paper."
    },
    "epistemic_to_modal_transition": {
      "description": "Recast knowledge and common knowledge in modal/fixed-point terms.",
      "paper_alignment": "Common knowledge operator is defined and analyzed formally."
    },
    "local_posterior_to_global_agreement_transition": {
      "description": "Show that common knowledge of posteriors forces equality of beliefs.",
      "paper_alignment": "Formal proof of the agreement theorem."
    }
  },

  "ai.operators": {
    "knowledge_operator": {
      "type": "operator",
      "role": "Maps events to what an agent knows at a given information partition."
    },
    "common_knowledge_operator": {
      "type": "operator",
      "role": "Computes the greatest fixed point representing common knowledge of an event."
    },
    "posterior_operator": {
      "type": "operator",
      "role": "Assigns Bayesian posteriors to agents given their information sets."
    },
    "formal_proof_operator": {
      "type": "operator",
      "role": "Encodes the agreement theorem as a machine-checked proof object."
    }
  },

  "ai.audience": "Researchers in epistemic logic, game theory, formal verification, and AI alignment.",
  "ai.contact.github": "https://github.com/TriadicFrameworks",
  "ai.license": "Open educational use permitted"
}