{
  "title": "Defects Generalized Symmetry Categorical Qft Dependency Map",
  "question": "Which one-way hypotheses connect typed defect strata to coherent fusion and junctions, a categorical action, anomaly-free gauging or condensation, relative boundary data, and a bounded classification statement?",
  "takeaway": "Source–target and link compatibility make composition meaningful; pentagon, unit, and duality identities make it coherent; a module category supplies an action; crossed or algebra-object obstruction tests license gauging or condensation; relative boundary data license interfaces; and the final conclusion remains at the explicitly named equivalence and realization level.",
  "figure_type": "dependency",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "n0",
      "label": "stratified defect data\\\\phases, oriented defects, and junctions\\\\typed links and bordism gluing"
    },
    {
      "id": "n1",
      "label": "coherent fusion structure\\\\associators, units, duals, pivotal or braided data\\\\all pentagon, triangle, and snake identities"
    },
    {
      "id": "n2",
      "label": "categorical action\\\\module and bimodule categories\\\\higher representations and selection rules"
    },
    {
      "id": "n3",
      "label": "admissible theory change\\\\anomaly-free crossed action or separable local algebra\\\\equivariantization, gauging, orbifold, or condensation"
    },
    {
      "id": "n4",
      "label": "relative boundary system\\\\symmetry TFT, polarization, and interfaces\\\\matched anomalies and tangential structures"
    },
    {
      "id": "n5",
      "label": "bounded conclusion\\\\named categorical equivalence and realization functor\\\\no automatic local-QFT converse"
    },
    {
      "id": "branch",
      "label": "group-like objects $\\Rightarrow$ invertible $p$-form symmetry\\\\direct-sum fusion $\\Rightarrow$ noninvertible symmetry\\\\nonsemisimple category $\\Rightarrow$ extensions and modified traces"
    }
  ],
  "edges": [
    {
      "from": "n0",
      "to": "n1",
      "label": "type",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "n2",
      "label": "cohere",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "n3",
      "label": "act",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "n4",
      "label": "change",
      "logical_status": "licensed implication"
    },
    {
      "from": "n4",
      "to": "n5",
      "label": "classify",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "branch",
      "label": "special regimes",
      "logical_status": "licensed implication"
    }
  ]
}