{
  "title": "Representative claim domains and validity boundaries for Modular Response, Relative Entropy, and Emergent-Gravity Claims",
  "table_id": "modular-response-relative-entropy-and-emergent-gravity-claims-claim-domain-table",
  "columns": [
    {
      "key": "claim_object",
      "label": "Claim object"
    },
    {
      "key": "state_ensemble_and_conventions",
      "label": "State, ensemble, and conventions"
    },
    {
      "key": "approximation_status_and_evidence_timing",
      "label": "Approximation, status, and evidence timing"
    },
    {
      "key": "uncertainty_and_counterevidence",
      "label": "Uncertainty and counterevidence"
    },
    {
      "key": "falsifier",
      "label": "Falsifier"
    },
    {
      "key": "failure_condition",
      "label": "Failure condition"
    },
    {
      "key": "licensed_conclusion",
      "label": "Licensed conclusion"
    }
  ],
  "records": [
    {
      "claim_object": {
        "text": "entanglement first law",
        "html": "entanglement first law"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare reference state and modular operator; use the volume conventions unless the page states a local replacement.",
        "html": "Declare reference state and modular operator; use the volume conventions unless the page states a local replacement."
      },
      "approximation_status_and_evidence_timing": {
        "text": "Model-specific calculation or conditional result. Control chain: boundary relative entropy → modular flow and first law → bulk canonical energy → positivity and shape checks → conditional gravity inference. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Model-specific calculation or conditional result. Control chain: boundary relative entropy → modular flow and first law → bulk canonical energy → positivity and shape checks → conditional gravity inference. Sources are cited on the destination page; literature checked through 10 August 2026."
      },
      "uncertainty_and_counterevidence": {
        "text": "Track omitted corrections, alternate branches, and competing definitions. A failed “linear-response identity” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “linear-response identity” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "linear-response identity",
        "html": "linear-response identity"
      },
      "failure_condition": {
        "text": "nonlinear field equations",
        "html": "nonlinear field equations"
      },
      "licensed_conclusion": {
        "text": "first-order entropy relation",
        "html": "first-order entropy relation"
      }
    },
    {
      "claim_object": {
        "text": "relative-entropy equality",
        "html": "relative-entropy equality"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare boundary and bulk algebras plus area term; use the volume conventions unless the page states a local replacement.",
        "html": "Declare boundary and bulk algebras plus area term; use the volume conventions unless the page states a local replacement."
      },
      "approximation_status_and_evidence_timing": {
        "text": "Model-specific calculation or conditional result. Control chain: boundary relative entropy → modular flow and first law → bulk canonical energy → positivity and shape checks → conditional gravity inference. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Model-specific calculation or conditional result. Control chain: boundary relative entropy → modular flow and first law → bulk canonical energy → positivity and shape checks → conditional gravity inference. Sources are cited on the destination page; literature checked through 10 August 2026."
      },
      "uncertainty_and_counterevidence": {
        "text": "Track omitted corrections, alternate branches, and competing definitions. A failed “second-order positivity check” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “second-order positivity check” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "second-order positivity check",
        "html": "second-order positivity check"
      },
      "failure_condition": {
        "text": "exact equality for all states",
        "html": "exact equality for all states"
      },
      "licensed_conclusion": {
        "text": "canonical-energy relation in a code sector",
        "html": "canonical-energy relation in a code sector"
      }
    },
    {
      "claim_object": {
        "text": "field-equation inference",
        "html": "field-equation inference"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare all balls or shapes and local dynamics assumptions; use the volume conventions unless the page states a local replacement.",
        "html": "Declare all balls or shapes and local dynamics assumptions; use the volume conventions unless the page states a local replacement."
      },
      "approximation_status_and_evidence_timing": {
        "text": "Model-specific calculation or conditional result. Control chain: boundary relative entropy → modular flow and first law → bulk canonical energy → positivity and shape checks → conditional gravity inference. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Model-specific calculation or conditional result. Control chain: boundary relative entropy → modular flow and first law → bulk canonical energy → positivity and shape checks → conditional gravity inference. Sources are cited on the destination page; literature checked through 10 August 2026."
      },
      "uncertainty_and_counterevidence": {
        "text": "Track omitted corrections, alternate branches, and competing definitions. A failed “constraint and boundary-term check” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “constraint and boundary-term check” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "constraint and boundary-term check",
        "html": "constraint and boundary-term check"
      },
      "failure_condition": {
        "text": "a unique quantum-gravity action",
        "html": "a unique quantum-gravity action"
      },
      "licensed_conclusion": {
        "text": "conditional linearized equations",
        "html": "conditional linearized equations"
      }
    }
  ],
  "scope": "Exact structured equivalent of the reader-facing semantic table; column order, cell text, and source HTML are preserved."
}