{
  "title": "Holographic Entropy and Quantum Extremal Geometry: validity and failure map",
  "chapter": "Holographic Entropy and Quantum Extremal Geometry",
  "kind": "validity-failure",
  "schematic": true,
  "not_to_scale": true,
  "stages": [
    "regulated state and entropy",
    "extremal or generalized functional",
    "replica and surface selection",
    "maximin and correction checks",
    "geometric entropy claim"
  ],
  "claims": [
    {
      "object": "RT or HRT surface",
      "required_declaration": "state, region, homology, and causal setting",
      "diagnostic": "maximin and competing-surface check",
      "licensed_conclusion": "leading semiclassical entropy",
      "unsupported_promotion": "exact finite-N entropy"
    },
    {
      "object": "FLM or QES",
      "required_declaration": "bulk entropy scheme and Newton coupling",
      "diagnostic": "generalized-entropy extremization",
      "licensed_conclusion": "stated quantum correction",
      "unsupported_promotion": "microscopic factorization"
    },
    {
      "object": "replica derivation",
      "required_declaration": "integer replicas and continuation rule",
      "diagnostic": "cone regularity and saddle competition",
      "licensed_conclusion": "conditional analytic continuation",
      "unsupported_promotion": "unique nonperturbative continuation"
    }
  ],
  "takeaway": "RT, HRT, FLM, and QES are distinct prescriptions with different orders in gravity, saddle choices, and renormalization requirements."
}