{
  "title": "Representative claim domains and validity boundaries for Thermal Phases and AdS Black Holes",
  "table_id": "thermal-phases-and-ads-black-holes-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": "Hawking-Page transition",
        "html": "Hawking-Page transition"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare boundary topology and canonical ensemble; use the volume conventions unless the page states a local replacement.",
        "html": "Declare boundary topology and canonical ensemble; 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: ensemble and boundary data → Euclidean gravitational saddles → action, entropy, and charges → stability and finite-N checks → thermal phase claim. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Model-specific calculation or conditional result. Control chain: ensemble and boundary data → Euclidean gravitational saddles → action, entropy, and charges → stability and finite-N checks → thermal phase claim. 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 “renormalized free-energy crossing” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “renormalized free-energy crossing” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "renormalized free-energy crossing",
        "html": "renormalized free-energy crossing"
      },
      "failure_condition": {
        "text": "a sharp finite-N transition",
        "html": "a sharp finite-N transition"
      },
      "licensed_conclusion": {
        "text": "dominant semiclassical saddle",
        "html": "dominant semiclassical saddle"
      }
    },
    {
      "claim_object": {
        "text": "charged or rotating saddle",
        "html": "charged or rotating saddle"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare chemical potentials and regularity; use the volume conventions unless the page states a local replacement.",
        "html": "Declare chemical potentials and regularity; 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: ensemble and boundary data → Euclidean gravitational saddles → action, entropy, and charges → stability and finite-N checks → thermal phase claim. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Model-specific calculation or conditional result. Control chain: ensemble and boundary data → Euclidean gravitational saddles → action, entropy, and charges → stability and finite-N checks → thermal phase claim. 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 “first law and Hessian stability” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “first law and Hessian stability” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "first law and Hessian stability",
        "html": "first law and Hessian stability"
      },
      "failure_condition": {
        "text": "global stability in every ensemble",
        "html": "global stability in every ensemble"
      },
      "licensed_conclusion": {
        "text": "thermodynamics in a stated ensemble",
        "html": "thermodynamics in a stated ensemble"
      }
    },
    {
      "claim_object": {
        "text": "higher-derivative entropy",
        "html": "higher-derivative entropy"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare covariant action and boundary terms; use the volume conventions unless the page states a local replacement.",
        "html": "Declare covariant action and boundary terms; 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: ensemble and boundary data → Euclidean gravitational saddles → action, entropy, and charges → stability and finite-N checks → thermal phase claim. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Model-specific calculation or conditional result. Control chain: ensemble and boundary data → Euclidean gravitational saddles → action, entropy, and charges → stability and finite-N checks → thermal phase claim. 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 “Wald and Euclidean checks” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “Wald and Euclidean checks” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "Wald and Euclidean checks",
        "html": "Wald and Euclidean checks"
      },
      "failure_condition": {
        "text": "microscopic state counting",
        "html": "microscopic state counting"
      },
      "licensed_conclusion": {
        "text": "corrected saddle entropy",
        "html": "corrected saddle entropy"
      }
    }
  ],
  "scope": "Exact structured equivalent of the reader-facing semantic table; column order, cell text, and source HTML are preserved."
}