{
  "title": "Holographic Complexity Proposals and Diagnostics: validity and failure map",
  "chapter": "Holographic Complexity Proposals and Diagnostics",
  "kind": "validity-failure",
  "schematic": true,
  "not_to_scale": true,
  "stages": [
    "boundary complexity task",
    "CV, CA, or path proposal",
    "regulator and counterterms",
    "growth and switchback tests",
    "proposal comparison"
  ],
  "claims": [
    {
      "object": "complexity equals volume",
      "required_declaration": "slice, length scale, and subtraction",
      "diagnostic": "late-growth and formation checks",
      "licensed_conclusion": "one geometric proposal",
      "unsupported_promotion": "the same observable as action"
    },
    {
      "object": "complexity equals action",
      "required_declaration": "WdW patch and null-boundary terms",
      "diagnostic": "joint, counterterm, and switchback check",
      "licensed_conclusion": "one action-based proposal",
      "unsupported_promotion": "scheme-independent complexity"
    },
    {
      "object": "complexity bound",
      "required_declaration": "gate set or bulk prescription",
      "diagnostic": "counterexample and normalization test",
      "licensed_conclusion": "a bound in the stated model",
      "unsupported_promotion": "a universal operational theorem"
    }
  ],
  "takeaway": "CV, CA, path-integral, and tensor-network prescriptions are inequivalent conjectures whose divergences and operational meaning must be compared."
}