{
  "title": "Factorization Algebras Dependency Map",
  "question": "Which one-way hypotheses lead from disjoint-region operations through Weiss descent and field-theoretic observables to perturbative quantization, locally constant higher algebra, factorization homology, and the restricted Lorentzian AQFT comparison?",
  "takeaway": "Prefactorization operations become a factorization algebra only after derived Weiss descent; elliptic or Green-hyperbolic field data then supply classical observables; local BV cohomology governs perturbative quantization; and locally constant or Lorentzian comparison conclusions require their own tangential, additivity, Cauchy-constancy, and time-orderability hypotheses.",
  "figure_type": "dependency",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "n0",
      "label": "prefactorization data\\\\opens and disjoint tuples\\\\coherent maps in $(\\mathcal C,\\otimes)$"
    },
    {
      "id": "n1",
      "label": "Weiss descent\\\\finite configurations lie in one cover member\\\\derived Cech reconstruction"
    },
    {
      "id": "n2",
      "label": "field complex\\\\elliptic BV or Green-hyperbolic data\\\\support, quotient, wavefront domain"
    },
    {
      "id": "n3",
      "label": "classical observables\\\\shifted BV or Peierls bracket\\\\local-to-global cochain model"
    },
    {
      "id": "n4",
      "label": "quantum observables\\\\local obstruction vanishes or is cancelled\\\\effective QME and RG compatibility"
    },
    {
      "id": "n5",
      "label": "restricted comparison\\\\additivity, Cauchy constancy, time ordering\\\\strict AQFT equivalence in stated target"
    },
    {
      "id": "branch",
      "label": "local constancy plus tangential structure $\\Rightarrow E_n$ algebra\\\\tensor excision and colimits $\\Rightarrow \\int_M A$\\\\holomorphic or twisted models need their own anomaly checks"
    }
  ],
  "edges": [
    {
      "from": "n0",
      "to": "n1",
      "label": "prove descent",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "n2",
      "label": "choose theory",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "n3",
      "label": "construct bracket",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "n4",
      "label": "renormalize",
      "logical_status": "licensed implication"
    },
    {
      "from": "n4",
      "to": "n5",
      "label": "add Lorentzian data",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "branch",
      "label": "topological branch",
      "logical_status": "licensed implication"
    }
  ]
}