{
  "title": "Scattering Infrared Particle Structure Dependency Map",
  "question": "Which spectral, locality, and asymptotic hypotheses lead from a stable mass shell to scattering states, LSZ limits, and qualified analytic conclusions?",
  "takeaway": "An isolated mass shell and locality support Haag--Ruelle limits and isometric Møller maps; completeness is extra, while failure of a sharp charged shell redirects the theory to detector, radiation, sector, dressed, or inclusive objects.",
  "figure_type": "dependency",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "n0",
      "label": "translation spectrum $E(\\cdot)$\\\\test for isolated $H_m$"
    },
    {
      "id": "n1",
      "label": "one-particle space $\\mathcal H_1$\\\\finite-energy core $\\mathcal D_E$"
    },
    {
      "id": "n2",
      "label": "Haag--Ruelle products $A_{k,t}(f_k)$\\\\disjoint velocity supports"
    },
    {
      "id": "n3",
      "label": "Møller maps $\\Omega_{\\rm in/out}$\\\\isometries, not yet onto"
    },
    {
      "id": "n4",
      "label": "LSZ boundary values\\\\stable-pole distributional limits"
    },
    {
      "id": "n5",
      "label": "analytic amplitude domains\\\\qualified crossing and bounds"
    },
    {
      "id": "branch",
      "label": "infrared alternatives\\\\detectors, weights, radiation\\\\sectors, dressed or inclusive data"
    }
  ],
  "edges": [
    {
      "from": "n0",
      "to": "n1",
      "label": "project",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "n2",
      "label": "locality",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "n3",
      "label": "strong limits",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "n4",
      "label": "amputate",
      "logical_status": "licensed implication"
    },
    {
      "from": "n4",
      "to": "n5",
      "label": "analyticity",
      "logical_status": "licensed implication"
    },
    {
      "from": "n0",
      "to": "branch",
      "label": "no sharp charged shell",
      "logical_status": "conditional branch"
    }
  ]
}