{
  "title": "Extended Tqft Bordism Dependency Map",
  "question": "Which one-way hypotheses connect a declared structured bordism problem to a target higher category, successive duals and adjoints, the framed cobordism hypothesis, tangential refinements, invertible or relative theories, positivity, and a correctly typed classification claim?",
  "takeaway": "Dimension, tangential structure, extension depth, and bordism category fix the domain; a specified symmetric monoidal higher category fixes the target and equivalence; duals and adjoints through the visible level identify the fully dualizable objects classified by the framed fully extended theorem, while homotopy fixed points, Picard invertibility, relative anomaly data, reflection positivity, boundary modules, and microscopic realization are separate refinements rather than automatic consequences.",
  "figure_type": "dependency",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "n0",
      "label": "classification input\\\\dimension $n$, structure $\\xi$, depth $k$\\\\declared bordism category"
    },
    {
      "id": "n1",
      "label": "typed functor\\\\$Z:\\operatorname{Bord}^{\\xi}_{n,\\le k}\\to\\mathcal C$\\\\specified target and equivalence"
    },
    {
      "id": "n2",
      "label": "duality checks\\\\object duals and successive adjoints\\\\coherent through level $k$"
    },
    {
      "id": "n3",
      "label": "framed fully extended theorem\\\\fully dualizable point object\\\\functor groupoid up to equivalence"
    },
    {
      "id": "n4",
      "label": "structured refinements\\\\$G$ homotopy fixed point\\\\invertibility and positivity separate"
    },
    {
      "id": "n5",
      "label": "licensed conclusion\\\\exact theory class and equivalence\\\\physical realization still separate"
    },
    {
      "id": "branch",
      "label": "Picard target: spectrum map\\\\relative anomaly: boundary of invertible bulk\\\\reflection positivity: dagger plus positive doubles"
    }
  ],
  "edges": [
    {
      "from": "n0",
      "to": "n1",
      "label": "type",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "n2",
      "label": "adjoints",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "n3",
      "label": "classify",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "n4",
      "label": "refine",
      "logical_status": "licensed implication"
    },
    {
      "from": "n4",
      "to": "n5",
      "label": "scope",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "branch",
      "label": "specialize separately",
      "logical_status": "conditional branch"
    }
  ]
}