{
  "title": "Axioms Reconstruction Dependency Map",
  "question": "Which Wightman hypotheses lead to reconstruction, analyticity, CPT, and spin-statistics conclusions?",
  "takeaway": "Vacuum distributions inherit the field axioms; positivity reconstructs the cyclic theory, while spectral support and locality drive a separate analytic chain to the structural theorems.",
  "figure_type": "dependency",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "n0",
      "label": "operator-valued fields\\\\common invariant domain"
    },
    {
      "id": "n1",
      "label": "full vacuum hierarchy $W_n$\\\\tempered, covariant, local"
    },
    {
      "id": "n2",
      "label": "relative spectral support\\\\$(\\overline V_+)^{n-1}$"
    },
    {
      "id": "n3",
      "label": "primitive and extended tubes\\\\tempered boundary values"
    },
    {
      "id": "n4",
      "label": "Jost configurations\\\\edge-of-the-wedge continuation"
    },
    {
      "id": "n5",
      "label": "CPT and spin--statistics\\\\theorem-specific conclusions"
    },
    {
      "id": "branch",
      "label": "cyclic reconstruction\\\\$\\mathcal H,\\Omega,U,\\phi$\\\\unique up to unitary"
    }
  ],
  "edges": [
    {
      "from": "n0",
      "to": "n1",
      "label": "vacuum expectation",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "n2",
      "label": "spectrum condition",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "n3",
      "label": "Fourier--Laplace",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "n4",
      "label": "local equality",
      "logical_status": "licensed implication"
    },
    {
      "from": "n4",
      "to": "n5",
      "label": "complex covariance",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "branch",
      "label": "positivity plus all axioms",
      "logical_status": "licensed implication"
    }
  ]
}