{
  "title": "Existence Classification Problems Dependency Map",
  "question": "Which model, dimension, regulator, limit topology, reconstruction hypotheses, physical-property theorems, comparison maps, and dated sources are needed before an existence or classification claim in mathematical QFT is licensed?",
  "takeaway": "Existence, reconstruction, mass gaps or confinement observables, and classification are distinct theorem stages: low-dimensional constructive models traverse model-specific parts of the chain, while four-dimensional scalar, pure Yang--Mills, chiral-gauge, and categorical claims stop at explicitly dated obligations.",
  "figure_type": "dependency",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "n0",
      "label": "typed frontier claim\\\\model, dimension, regulator\\\\observable and topology fixed"
    },
    {
      "id": "n1",
      "label": "regulated construction\\\\positive measure or local algebra\\\\limit order declared"
    },
    {
      "id": "n2",
      "label": "continuum or reconstruction\\\\tightness, full correlations, positivity\\\\unique target object"
    },
    {
      "id": "n3",
      "label": "spectral or physical property\\\\gap, scattering, sectors, confinement\\\\separate theorem"
    },
    {
      "id": "n4",
      "label": "comparison or classification\\\\functors, essential image, realization\\\\converses tested"
    },
    {
      "id": "n5",
      "label": "dated conclusion\\\\proved partial result and obstruction\\\\open lemma plus physical destination"
    },
    {
      "id": "branch",
      "label": "low-dimensional exact and constructive models\\\\4D scalar, Yang--Mills, and chiral dossiers\\\\net--VOA, TQFT, and categorical classifications"
    }
  ],
  "edges": [
    {
      "from": "n0",
      "to": "n1",
      "label": "specify",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "n2",
      "label": "control",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "n3",
      "label": "reconstruct",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "n4",
      "label": "compare",
      "logical_status": "licensed implication"
    },
    {
      "from": "n4",
      "to": "n5",
      "label": "date",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "branch",
      "label": "three noninterchangeable frontiers",
      "logical_status": "licensed implication"
    }
  ]
}