{
  "title": "Wormholes, Gravitational Path Integrals, and Ensembles: structure map",
  "chapter": "Wormholes, Gravitational Path Integrals, and Ensembles",
  "kind": "structure",
  "schematic": true,
  "not_to_scale": true,
  "stages": [
    "boundary conditions and contour",
    "saddles and negative modes",
    "topology or replica sum",
    "factorization and alpha-sector tests",
    "completion claim"
  ],
  "claims": [
    {
      "object": "Euclidean wormhole",
      "required_declaration": "boundary data, measure, and cycle",
      "diagnostic": "negative-mode and steepest-descent check",
      "licensed_conclusion": "a saddle contribution",
      "unsupported_promotion": "a convergent gravitational path integral"
    },
    {
      "object": "replica wormhole",
      "required_declaration": "replica boundary conditions and continuation",
      "diagnostic": "saddle competition and entropy check",
      "licensed_conclusion": "a semiclassical replica contribution",
      "unsupported_promotion": "microscopic evaporation dynamics"
    },
    {
      "object": "factorization statement",
      "required_declaration": "fixed theory, ensemble, or alpha sector",
      "diagnostic": "multi-boundary connectedness test",
      "licensed_conclusion": "the declared factorization property",
      "unsupported_promotion": "automatic ensemble averaging"
    }
  ],
  "takeaway": "A wormhole contribution is defined only with a contour and theory; connected boundaries do not by themselves establish an ensemble or a fixed-theory completion."
}