{
  "title": "Causal Perturbation Theory Dependency Map",
  "question": "Which support, microlocal, extension, and normalization hypotheses lead from local functionals to a formal interacting net?",
  "takeaway": "Causal induction fixes time ordering off diagonals, finite-scaling-degree extension supplies controlled local freedom, and only normalized products and the Bogoliubov map produce a local formal net; Ward and background conditions are additional constraints.",
  "figure_type": "dependency",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "n0",
      "label": "local functionals and supports\\\\equicausal microcausal domain"
    },
    {
      "id": "n1",
      "label": "local $S$-matrix $S(F)$\\\\causal factorization"
    },
    {
      "id": "n2",
      "label": "Epstein--Glaser induction\\\\off-diagonal $T_n^0$"
    },
    {
      "id": "n3",
      "label": "scaling-degree extension\\\\finite local diagonal freedom"
    },
    {
      "id": "n4",
      "label": "renormalized $T_n$ and $Z$\\\\Bogoliubov map $R_V$"
    },
    {
      "id": "n5",
      "label": "scoped output\\\\local formal net or separate C*-net theorem"
    },
    {
      "id": "branch",
      "label": "Ward cohomology and perturbative agreement\\\\extra local renormalization conditions"
    }
  ],
  "edges": [
    {
      "from": "n0",
      "to": "n1",
      "label": "define",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "n2",
      "label": "factorize",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "n3",
      "label": "extend",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "n4",
      "label": "normalize",
      "logical_status": "licensed implication"
    },
    {
      "from": "n4",
      "to": "n5",
      "label": "qualify",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "branch",
      "label": "constraint path",
      "logical_status": "licensed implication"
    }
  ]
}