{
  "title": "Representative claim domains and validity boundaries for AdS3/CFT2 and Three-Dimensional Gravity",
  "table_id": "low-dimensional-holography-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": "Brown-Henneaux symmetry",
        "html": "Brown-Henneaux symmetry"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare boundary falloffs and charge normalization; use the volume conventions unless the page states a local replacement.",
        "html": "Declare boundary falloffs and charge normalization; use the volume conventions unless the page states a local replacement."
      },
      "approximation_status_and_evidence_timing": {
        "text": "Conditional theorem or structural result. Control chain: CFT2 and global data → AdS3 boundary conditions → Virasoro or Chern-Simons structure → BTZ and modular checks → three-dimensional gravity claim. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Conditional theorem or structural result. Control chain: CFT2 and global data → AdS3 boundary conditions → Virasoro or Chern-Simons structure → BTZ and modular checks → three-dimensional gravity 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 “central extension and integrability” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “central extension and integrability” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "central extension and integrability",
        "html": "central extension and integrability"
      },
      "failure_condition": {
        "text": "a complete Hilbert space",
        "html": "a complete Hilbert space"
      },
      "licensed_conclusion": {
        "text": "asymptotic Virasoro algebra",
        "html": "asymptotic Virasoro algebra"
      }
    },
    {
      "claim_object": {
        "text": "BTZ saddle",
        "html": "BTZ saddle"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare ensemble, identifications, and spin; use the volume conventions unless the page states a local replacement.",
        "html": "Declare ensemble, identifications, and spin; 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: CFT2 and global data → AdS3 boundary conditions → Virasoro or Chern-Simons structure → BTZ and modular checks → three-dimensional gravity claim. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Model-specific calculation or conditional result. Control chain: CFT2 and global data → AdS3 boundary conditions → Virasoro or Chern-Simons structure → BTZ and modular checks → three-dimensional gravity 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 “thermodynamic and modular check” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “thermodynamic and modular check” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "thermodynamic and modular check",
        "html": "thermodynamic and modular check"
      },
      "failure_condition": {
        "text": "all heavy CFT states are BTZ geometries",
        "html": "all heavy CFT states are BTZ geometries"
      },
      "licensed_conclusion": {
        "text": "controlled black-hole sector",
        "html": "controlled black-hole sector"
      }
    },
    {
      "claim_object": {
        "text": "pure gravity proposal",
        "html": "pure gravity proposal"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare spectrum, topology sum, and global form; use the volume conventions unless the page states a local replacement.",
        "html": "Declare spectrum, topology sum, and global form; use the volume conventions unless the page states a local replacement."
      },
      "approximation_status_and_evidence_timing": {
        "text": "Proposal or conditional construction. Control chain: CFT2 and global data → AdS3 boundary conditions → Virasoro or Chern-Simons structure → BTZ and modular checks → three-dimensional gravity claim. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Proposal or conditional construction. Control chain: CFT2 and global data → AdS3 boundary conditions → Virasoro or Chern-Simons structure → BTZ and modular checks → three-dimensional gravity 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 “unitarity and modular consistency” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “unitarity and modular consistency” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "unitarity and modular consistency",
        "html": "unitarity and modular consistency"
      },
      "failure_condition": {
        "text": "established nonperturbative theory",
        "html": "established nonperturbative theory"
      },
      "licensed_conclusion": {
        "text": "a candidate partition function or sector",
        "html": "a candidate partition function or sector"
      }
    }
  ],
  "scope": "Exact structured equivalent of the reader-facing semantic table; column order, cell text, and source HTML are preserved."
}