{
  "schema": "abstraction-reading-map/v1",
  "date": "2026-10-07",
  "essay": "../essays/abstraction-is-compression.html",
  "purpose": "Navigation and claim-status metadata for human and agent readers. Not a Research Kernel MCP import or acceptance contract.",
  "formal_companion": {
    "source": "../proofs/abstraction/Abstraction.lean",
    "receipt": "../proofs/abstraction/verification.json",
    "readme": "../proofs/abstraction/README.md",
    "toolchain": "leanprover/lean4:v4.19.0",
    "public_theorems": 7,
    "axiom_policy": "No axiom dependencies for all seven statements."
  },
  "source_pins": {
    "CovertChannelLab": "ae90bb88273e82620f2e643c19f23aeea0d9b31c",
    "what-if-witness-spaces": "00dd88ededda2d771a56af071744bf6a07ae70fc"
  },
  "claims": [
    {
      "id": "decision-compression",
      "status": "proved_in_model",
      "claim": "If the answer factors through a summary, equal summaries preserve the chosen answer.",
      "theorems": [
        "compression_preserves_decision"
      ],
      "assumptions": [
        "A readout reproduces the answer for every concrete state."
      ],
      "scope": "One specified question; not lossless reconstruction of every fact.",
      "essay_anchor": "compression-model"
    },
    {
      "id": "sound-safety-abstraction",
      "status": "proved_in_model",
      "claim": "Abstract unreachability implies concrete unreachability when transitions and forbidden states are covered.",
      "theorems": [
        "reachability_maps",
        "abstract_safety_transfers",
        "omitted_edge_changes_answer"
      ],
      "assumptions": [
        "Every concrete step maps to an abstract step, including stuttering self-loops.",
        "Every concrete bad state maps to an abstract bad state.",
        "The abstract bad states are unreachable."
      ],
      "scope": "Finite execution prefixes of the supplied transition relations. Coverage of physical behavior remains a separate obligation.",
      "essay_anchor": "compression-model"
    },
    {
      "id": "intelligence-and-invariants",
      "status": "proved_in_model",
      "claim": "A closed invariant contains every reachable state, independently of which modeled strategy selects the steps.",
      "theorems": [
        "reachable_invariant"
      ],
      "assumptions": [
        "Initial state is inside the invariant.",
        "Every modeled transition preserves it."
      ],
      "scope": "No intelligence parameter or agent implementation is formalized; the quantification covers all supplied transitions.",
      "essay_anchor": "hypothesis"
    },
    {
      "id": "physical-containment-existence",
      "status": "hypothesis",
      "claim": "At least one useful admissible physical configuration exists that excludes every forbidden outcome for every physically available strategy under an explicit environment contract.",
      "formula": "exists c in C_E: (U_E(c) and (forall pi in Pi_E(c): not Escape_E(c,pi)))",
      "theorems": [],
      "assumptions": [
        "Specified physics and operating envelope.",
        "Useful-service predicate excludes switching the machine off.",
        "Forbidden outcomes, observers, actuators, lifetime, resources, maintenance, and outside assistance are defined."
      ],
      "scope": "Not established by the essay, the lab model, or the new Lean companion.",
      "essay_anchor": "quantified-model",
      "quantifier_note": "Existence, not uniqueness: the same chosen configuration must withstand every strategy in its modeled domain."
    },
    {
      "id": "existential-counterargument",
      "status": "proved_in_model",
      "claim": "Given at least one admissible configuration defeating all modeled strategies, universal escapability for that same design domain and environment is false.",
      "theorems": [
        "witness_refutes_universal_escape",
        "quantifier_order_matters"
      ],
      "assumptions": [
        "A witness with the universal safety property is supplied.",
        "A common strategy type encodes validity inside the escape predicate."
      ],
      "scope": "Logical consequence conditional on the witness. Does not establish the physical existence hypothesis.",
      "essay_anchor": "quantified-model"
    },
    {
      "id": "covert-channel-witness",
      "status": "replayed_model",
      "claim": "The pinned catalogue has 1760 configurations and 19 feasible designs; (s,r)=(7,2) attains the global integer cost lower bound 57.",
      "evidence": [
        "../proofs/abstraction/covert-replay.json",
        "https://github.com/TheDarkLightX/CovertChannelLab/blob/ae90bb88273e82620f2e643c19f23aeea0d9b31c/Proofs.lean",
        "https://github.com/TheDarkLightX/CovertChannelLab/blob/ae90bb88273e82620f2e643c19f23aeea0d9b31c/MATH.md"
      ],
      "assumptions": [
        "Five digital controls use the stated semantics.",
        "s,r are nonnegative integers; 2s+r>=16; service constraint r<=4.",
        "Cost J=s^2+2r^2 and service U=100-5r are stipulated."
      ],
      "scope": "Illustrative digital and thermal model, not measured hardware performance or production certification.",
      "essay_anchor": "lab-math"
    },
    {
      "id": "physical-refinement",
      "status": "open_refinement",
      "claim": "A model guarantee transfers to a deployed system only after concrete behavior and forbidden outcomes are covered by the verified abstraction.",
      "evidence": [
        "https://github.com/TheDarkLightX/CovertChannelLab/blob/ae90bb88273e82620f2e643c19f23aeea0d9b31c/CONTRACTS.md",
        "https://github.com/TheDarkLightX/CovertChannelLab/blob/ae90bb88273e82620f2e643c19f23aeea0d9b31c/MATH.md"
      ],
      "open_obligations": [
        "Measure and bound physical plant parameters across the operating envelope.",
        "Prove the real-valued thermal plant refines the Lean integer envelope.",
        "Implement and validate the trusted total fallback, canonical verifier, schedule, and resource partition.",
        "Inventory all observer and actuator channels, including raw physical sensors.",
        "Account separately for authorized harmful outputs, actions, and human operators."
      ],
      "scope": "These gates are not discharged by the model replay.",
      "essay_anchor": "proof-layer"
    },
    {
      "id": "autonomy-boundary-interaction",
      "status": "interpretation",
      "claim": "More independent choices and persistent shared search increase the importance of enforcing task boundaries and specifying stop conditions.",
      "evidence": [
        "https://openai.com/index/hugging-face-incident-and-the-road-ahead/",
        "https://metr.org/blog/2026-08-26-openai-hugging-face-incident-investigation/"
      ],
      "scope": "The reported incident involved existing isolation controls that failed. The causal interpretation is the author's synthesis, not a finding about a lab's intentions.",
      "essay_anchor": "autonomy"
    },
    {
      "id": "witness-search-method",
      "status": "research_method",
      "claim": "Alternate candidate synthesis with counterexample search, retaining valid failures as constraints for later designs.",
      "evidence": [
        "https://github.com/TheDarkLightX/what-if-witness-spaces/blob/00dd88ededda2d771a56af071744bf6a07ae70fc/paper/NEURO_SYMBOLIC_DISASTER_LOOP.md",
        "https://doi.org/10.5281/zenodo.19763921",
        "https://people.csail.mit.edu/asolar/SynthesisCourse2020/Lecture10.htm"
      ],
      "scope": "The preprint has a bounded, checker-relative witness language. Its archived result was not independently replayed for this essay. Search failure or timeout cannot establish universal safety.",
      "essay_anchor": "search-loop"
    }
  ],
  "abstraction_cards": "essay-abstractions.json"
}