{
  "title": "AdS Geometry, Boundary Problems, and the Dictionary: validity and failure map",
  "chapter": "AdS Geometry, Boundary Problems, and the Dictionary",
  "kind": "validity-failure",
  "schematic": true,
  "not_to_scale": true,
  "stages": [
    "AdS patch and conformal boundary",
    "boundary and global conditions",
    "asymptotic field modes",
    "renormalized source and response",
    "operator dictionary"
  ],
  "claims": [
    {
      "object": "scalar mode",
      "required_declaration": "mass, patch, and boundary condition",
      "diagnostic": "normalizability and flux test",
      "licensed_conclusion": "allowed source-response branch",
      "unsupported_promotion": "a branch outside its stability window"
    },
    {
      "object": "current or stress tensor",
      "required_declaration": "gauge group, charges, and counterterms",
      "diagnostic": "Ward identity and two-point normalization",
      "licensed_conclusion": "a normalized operator map",
      "unsupported_promotion": "complete global equivalence"
    },
    {
      "object": "state dictionary",
      "required_declaration": "Euclidean cap or Lorentzian initial data",
      "diagnostic": "causal and inner-product check",
      "licensed_conclusion": "a state in the declared sector",
      "unsupported_promotion": "all heavy states have smooth geometries"
    }
  ],
  "takeaway": "An AdS/CFT entry is defined by geometry, boundary conditions, global sector, quantization branch, and normalization—not by a mass-dimension formula alone."
}