{
  "title": "Representative claim domains and validity boundaries for AdS Geometry, Boundary Problems, and the Dictionary",
  "table_id": "ads-cft-dictionary-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": "scalar mode",
        "html": "scalar mode"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare mass, patch, and boundary condition; use the volume conventions unless the page states a local replacement.",
        "html": "Declare mass, patch, and boundary condition; 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: AdS patch and conformal boundary → boundary and global conditions → asymptotic field modes → renormalized source and response → operator dictionary. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Model-specific calculation or conditional result. Control chain: AdS patch and conformal boundary → boundary and global conditions → asymptotic field modes → renormalized source and response → operator dictionary. 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 “normalizability and flux test” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “normalizability and flux test” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "normalizability and flux test",
        "html": "normalizability and flux test"
      },
      "failure_condition": {
        "text": "a branch outside its stability window",
        "html": "a branch outside its stability window"
      },
      "licensed_conclusion": {
        "text": "allowed source-response branch",
        "html": "allowed source-response branch"
      }
    },
    {
      "claim_object": {
        "text": "current or stress tensor",
        "html": "current or stress tensor"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare gauge group, charges, and counterterms; use the volume conventions unless the page states a local replacement.",
        "html": "Declare gauge group, charges, and counterterms; 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: AdS patch and conformal boundary → boundary and global conditions → asymptotic field modes → renormalized source and response → operator dictionary. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Model-specific calculation or conditional result. Control chain: AdS patch and conformal boundary → boundary and global conditions → asymptotic field modes → renormalized source and response → operator dictionary. 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 “Ward identity and two-point normalization” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “Ward identity and two-point normalization” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "Ward identity and two-point normalization",
        "html": "Ward identity and two-point normalization"
      },
      "failure_condition": {
        "text": "complete global equivalence",
        "html": "complete global equivalence"
      },
      "licensed_conclusion": {
        "text": "a normalized operator map",
        "html": "a normalized operator map"
      }
    },
    {
      "claim_object": {
        "text": "state dictionary",
        "html": "state dictionary"
      },
      "state_ensemble_and_conventions": {
        "text": "Declare Euclidean cap or Lorentzian initial data; use the volume conventions unless the page states a local replacement.",
        "html": "Declare Euclidean cap or Lorentzian initial data; use the volume conventions unless the page states a local replacement."
      },
      "approximation_status_and_evidence_timing": {
        "text": "Dictionary entry or correspondence claim. Control chain: AdS patch and conformal boundary → boundary and global conditions → asymptotic field modes → renormalized source and response → operator dictionary. Sources are cited on the destination page; literature checked through 10 August 2026.",
        "html": "Dictionary entry or correspondence claim. Control chain: AdS patch and conformal boundary → boundary and global conditions → asymptotic field modes → renormalized source and response → operator dictionary. 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 “causal and inner-product check” check is counterevidence to the promoted claim.",
        "html": "Track omitted corrections, alternate branches, and competing definitions. A failed “causal and inner-product check” check is counterevidence to the promoted claim."
      },
      "falsifier": {
        "text": "causal and inner-product check",
        "html": "causal and inner-product check"
      },
      "failure_condition": {
        "text": "all heavy states have smooth geometries",
        "html": "all heavy states have smooth geometries"
      },
      "licensed_conclusion": {
        "text": "a state in the declared sector",
        "html": "a state in the declared sector"
      }
    }
  ],
  "scope": "Exact structured equivalent of the reader-facing semantic table; column order, cell text, and source HTML are preserved."
}