{
  "title": "Conformal Nets Vertex Algebras Dependency Map",
  "question": "Which interval-net, energy, additivity, split, index, sector, and Q-system hypotheses license rational chiral and full-CFT conclusions?",
  "takeaway": "Vacuum net axioms establish localization; split, strong additivity, and finite two-interval index jointly license modular DHR sectors, while a separate positive commutative Q-system is required for a local extension or full CFT.",
  "figure_type": "dependency",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "n0",
      "label": "proper intervals $I\\subset S^1$ and $\\mathcal A(I)$\\\\isotony, locality, vacuum, $L_0\\ge0$"
    },
    {
      "id": "n1",
      "label": "point and collar control\\\\strong additivity plus split"
    },
    {
      "id": "n2",
      "label": "two-interval subfactor\\\\finite $\\mu=[\\mathcal A(E')':\\mathcal A(E)]$"
    },
    {
      "id": "n3",
      "label": "localized transportable endomorphisms\\\\finite unitary modular DHR category"
    },
    {
      "id": "n4",
      "label": "positive commutative Q-system\\\\local finite-index extension"
    },
    {
      "id": "n5",
      "label": "left--right reverse braiding\\\\local full two-dimensional net"
    },
    {
      "id": "branch",
      "label": "infinite $\\mu$ or nonsemisimple input\\\\no finite modular-category conclusion"
    }
  ],
  "edges": [
    {
      "from": "n0",
      "to": "n1",
      "label": "add split",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "n2",
      "label": "define index",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "n3",
      "label": "classify",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "n4",
      "label": "extend",
      "logical_status": "licensed implication"
    },
    {
      "from": "n4",
      "to": "n5",
      "label": "full center",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "branch",
      "label": "nonrational branch",
      "logical_status": "licensed implication"
    }
  ]
}