{
  "title": "Theorem Frameworks Claim Grammar Dependency Map",
  "question": "Which typed objects, domains, quantifiers, hypotheses, proof routes, and source versions are needed before an existence, reconstruction, or framework-comparison claim in QFT has a determinate conclusion?",
  "takeaway": "A cutoff field family, a full Schwinger hierarchy, and a locally covariant functor enter different directional arguments: each must be typed on its own carrier, supplied with its exact hypotheses, and passed through a named construction before existence, reconstruction, comparison, or uniqueness language is licensed.",
  "figure_type": "dependency",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "n0",
      "label": "one candidate QFT object\\\\examples: $\\phi^4_{a,L}$, all $S_n$, BFV functor $\\mathcal A$"
    },
    {
      "id": "n1",
      "label": "domains and quantifiers\\\\$\\mathcal S$, $C_c^\\infty$, common core; $a\\downarrow0$ then $L\\uparrow\\infty$"
    },
    {
      "id": "n2",
      "label": "essential hypotheses\\\\OS positivity and growth; spectrum and locality; functorial time-slice"
    },
    {
      "id": "n3",
      "label": "named proof route\\\\Glimm--Jaffe estimates; OS quotient; BFV naturality"
    },
    {
      "id": "n4",
      "label": "licensed output\\\\continuum $S_n$; cyclic Wightman QFT; locally covariant net"
    },
    {
      "id": "n5",
      "label": "strength and source\\\\unitary or natural class; nonconverse; pinned theorem version"
    },
    {
      "id": "branch",
      "label": "Lean OSforGFF master\\\\$d=4$, $m>0$, commit 2f0965a\\\\encoded Gaussian OS predicates only"
    }
  ],
  "edges": [
    {
      "from": "n0",
      "to": "n1",
      "label": "carrier",
      "logical_status": "licensed implication"
    },
    {
      "from": "n1",
      "to": "n2",
      "label": "quantifiers",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "n3",
      "label": "hypotheses",
      "logical_status": "licensed implication"
    },
    {
      "from": "n3",
      "to": "n4",
      "label": "theorem",
      "logical_status": "licensed implication"
    },
    {
      "from": "n4",
      "to": "n5",
      "label": "scope",
      "logical_status": "licensed implication"
    },
    {
      "from": "n2",
      "to": "branch",
      "label": "kernel-checked free branch",
      "logical_status": "licensed implication"
    }
  ]
}