{
  "title": "Theorem Frameworks Claim Grammar Failure Map",
  "question": "Which concrete domain error, dropped hypothesis, substituted check, or false converse first breaks a proposed QFT theorem record?",
  "takeaway": "A shared two-point function does not identify frameworks, a plane wave or coincident product can leave the theorem's domain, pointwise covariance positivity does not supply reflection positivity, and neither a stable computation nor a successful build proves an unencoded theorem or converse.",
  "figure_type": "failure",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "a0",
      "row": "licensed implication",
      "label": "typed source object\\\\$\\phi^4_{a,L}$, full $S_n$, or $\\mathcal A:{\\rm Loc}\\to{\\rm Alg}$"
    },
    {
      "id": "a1",
      "row": "licensed implication",
      "label": "valid carrier and quantifiers\\\\test space, common domain, declared limit order"
    },
    {
      "id": "a2",
      "row": "licensed implication",
      "label": "complete hypotheses\\\\all-order OS positivity, uniform bounds, naturality"
    },
    {
      "id": "a3",
      "row": "licensed implication",
      "label": "exact proof or construction\\\\compactness, OS reconstruction, comparison theorem"
    },
    {
      "id": "a4",
      "row": "licensed implication",
      "label": "scoped conclusion\\\\existence or stated unitary or natural equivalence only"
    },
    {
      "id": "b0",
      "row": "first broken step",
      "label": "one shared $W_2$ called equivalence\\\\objects, morphisms, states, essential surjectivity missing"
    },
    {
      "id": "b1",
      "row": "first broken step",
      "label": "plane wave or coincident product; swap $a,L$ limits\\\\expression or convergence claim undefined"
    },
    {
      "id": "b2",
      "row": "first broken step",
      "label": "$C(p^2)>0$ with a negative residue; incompatible $S_4$\\\\no reflection or full polynomial positivity"
    },
    {
      "id": "b3",
      "row": "first broken step",
      "label": "stable simulation or build after weakening OS3\\\\check does not prove the intended theorem"
    },
    {
      "id": "b4",
      "row": "first broken step",
      "label": "local quasiequivalence called global unitary\\\\false converse or corrected hypothesis omitted"
    }
  ],
  "edges": [
    {
      "from": "a0",
      "to": "a1",
      "label": "state domains",
      "logical_status": "licensed implication"
    },
    {
      "from": "a1",
      "to": "a2",
      "label": "verify hypotheses",
      "logical_status": "licensed implication"
    },
    {
      "from": "a2",
      "to": "a3",
      "label": "apply named result",
      "logical_status": "licensed implication"
    },
    {
      "from": "a3",
      "to": "a4",
      "label": "state exact strength",
      "logical_status": "licensed implication"
    },
    {
      "from": "a0",
      "to": "b0",
      "label": "erase object class",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a1",
      "to": "b1",
      "label": "leave domain or swap quantifiers",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a2",
      "to": "b2",
      "label": "drop essential hypothesis",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a3",
      "to": "b3",
      "label": "substitute check for proof",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a4",
      "to": "b4",
      "label": "assert converse or ignore correction",
      "logical_status": "failure under removed or overstated hypothesis"
    }
  ]
}