{
  "title": "Scattering Infrared Particle Structure Failure Map",
  "question": "Which concrete test first exposes an illegal particle, completeness, infrared, or analyticity claim?",
  "takeaway": "A resonance is not a spectral subspace, a wave-operator isometry is not completeness, and neither charged infrared dressing nor massive analytic bounds survive outside their stated objects and domains.",
  "figure_type": "failure",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "a0",
      "row": "claim checkpoints",
      "label": "sharp particle $E(H_m)\\mathcal H$\\\\real isolated shell"
    },
    {
      "id": "a1",
      "row": "claim checkpoints",
      "label": "Haag--Ruelle limit on $\\mathcal D_E$\\\\locality, separated velocities"
    },
    {
      "id": "a2",
      "row": "claim checkpoints",
      "label": "Møller or LSZ output\\\\specified strong or weak limit"
    },
    {
      "id": "a3",
      "row": "claim checkpoints",
      "label": "infrared alternatives\\\\detectors, sectors, dressed or inclusive"
    },
    {
      "id": "a4",
      "row": "claim checkpoints",
      "label": "analytic boundary value\\\\massive proved domain"
    },
    {
      "id": "b0",
      "row": "first broken step",
      "label": "resonance or charged threshold\\\\no nonzero shell projection"
    },
    {
      "id": "b1",
      "row": "first broken step",
      "label": "overlapping velocities\\\\Cook estimate no longer closes"
    },
    {
      "id": "b2",
      "row": "first broken step",
      "label": "isometry called onto; absent electron pole\\\\completeness or LSZ is unproved"
    },
    {
      "id": "b3",
      "row": "first broken step",
      "label": "compact charge; dressed equals inclusive\\\\Gauss law or purity test fails"
    },
    {
      "id": "b4",
      "row": "first broken step",
      "label": "massless forward pole or global crossing\\\\gap or domain hypothesis fails"
    }
  ],
  "edges": [
    {
      "from": "a0",
      "to": "a1",
      "label": "local limit",
      "logical_status": "ordered diagnostic sequence, not implication across object classes"
    },
    {
      "from": "a1",
      "to": "a2",
      "label": "range or reduction",
      "logical_status": "ordered diagnostic sequence, not implication across object classes"
    },
    {
      "from": "a2",
      "to": "a3",
      "label": "infrared identity",
      "logical_status": "ordered diagnostic sequence, not implication across object classes"
    },
    {
      "from": "a3",
      "to": "a4",
      "label": "analytic domain",
      "logical_status": "ordered diagnostic sequence, not implication across object classes"
    },
    {
      "from": "a0",
      "to": "b0",
      "label": "replace real shell by continuation",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a1",
      "to": "b1",
      "label": "drop velocity separation",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a2",
      "to": "b2",
      "label": "assert a false converse",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a3",
      "to": "b3",
      "label": "identify inequivalent infrared objects",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a4",
      "to": "b4",
      "label": "leave the proved domain",
      "logical_status": "failure under removed or overstated hypothesis"
    }
  ]
}