{
  "title": "Causal Perturbation Theory Failure Map",
  "question": "Which dropped hypothesis first invalidates a causal product, extension, symmetry condition, or interacting-net claim?",
  "takeaway": "Causal order, compatible wavefront sets, finite scaling degree with local normalization, cohomologically admissible constraints, and separate infrared or nuclearity input fail in different ways and license different downgrades.",
  "figure_type": "failure",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "a0",
      "row": "licensed checkpoints",
      "label": "causal local S-matrix\\\\ordered compact supports"
    },
    {
      "id": "a1",
      "row": "licensed checkpoints",
      "label": "equicausal Peierls domain\\\\wavefront and equicontinuity control"
    },
    {
      "id": "a2",
      "row": "licensed checkpoints",
      "label": "diagonal extension and $Z$\\\\finite scaling, local freedom"
    },
    {
      "id": "a3",
      "row": "licensed checkpoints",
      "label": "Ward or background condition\\\\trivial class, controlled Møller map"
    },
    {
      "id": "a4",
      "row": "licensed checkpoints",
      "label": "scoped interacting output\\\\local formal or proved C*-net"
    },
    {
      "id": "b0",
      "row": "first broken step",
      "label": "overlapping unordered supports\\\\no licensed factorization"
    },
    {
      "id": "b1",
      "row": "first broken step",
      "label": "pointwise-only or characteristic smearing\\\\not smooth or product undefined"
    },
    {
      "id": "b2",
      "row": "first broken step",
      "label": "false uniqueness or nonlocal $Z$\\\\ambiguity hidden or locality lost"
    },
    {
      "id": "b3",
      "row": "first broken step",
      "label": "nontrivial anomaly or noncompact split\\\\identity or agreement obstructed"
    },
    {
      "id": "b4",
      "row": "first broken step",
      "label": "massless global limit or no regular strip\\\\no global state or compact locality theorem"
    }
  ],
  "edges": [
    {
      "from": "a0",
      "to": "a1",
      "label": "functional domain",
      "logical_status": "ordered diagnostic sequence, not a universal implication chain"
    },
    {
      "from": "a1",
      "to": "a2",
      "label": "renormalize",
      "logical_status": "ordered diagnostic sequence, not a universal implication chain"
    },
    {
      "from": "a2",
      "to": "a3",
      "label": "constrain",
      "logical_status": "ordered diagnostic sequence, not a universal implication chain"
    },
    {
      "from": "a3",
      "to": "a4",
      "label": "scope",
      "logical_status": "ordered diagnostic sequence, not a universal implication chain"
    },
    {
      "from": "a0",
      "to": "b0",
      "label": "drop order",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a1",
      "to": "b1",
      "label": "leave domain",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a2",
      "to": "b2",
      "label": "misuse freedom",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a3",
      "to": "b3",
      "label": "ignore obstruction",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a4",
      "to": "b4",
      "label": "overstate output",
      "logical_status": "failure under removed or overstated hypothesis"
    }
  ]
}