{
  "target_id": "corol form 1",
  "proof_status": "needs_context",
  "summary": "The supplied excerpt states the pairing formula but contains neither its proof nor the definitions needed to compute it. The introductory material does not establish these values. No contradiction is apparent from the statement alone; the missing proof anchor is a mapping limitation, not evidence of a proof defect. No external results have been imported.",
  "used_dependencies": [],
  "missing_context": [
    "Definition of \\mathcal{N}_1(1,n,n), including the permitted values of n and its defining monodromy matrices.",
    "Definition of v and the normalization and bilinear-pairing convention for (\\cdot,\\cdot).",
    "Confirmation that B belongs to the relevant form-preserving group.",
    "The preceding result or direct computation yielding the required orbit pairings, together with the intended proof anchor."
  ],
  "findings": [
    {
      "kind": "context",
      "source_quote": "Let $(\n\\cdot,\\cdot)$ be the normalized quadratic form preserved by $\\mathcal{N}_1(1,n,n)$.",
      "explanation": "The packet does not define the family \\mathcal{N}_1, its admissible values of n, the vector v, or the normalization convention. Although B is introduced generally as a local monodromy, its matrix for this family and its relationship to v are absent. Consequently, neither preservation of this particular form by B nor the diagonal value -2 can be checked."
    },
    {
      "kind": "unverified",
      "source_quote": "-3 & \\text{ if }& |i-j|=1\\\\\n-4 & \\text{ if }& |i-j|\\ge 2",
      "explanation": "No supplied calculation establishes either off-diagonal value. Conditional on B being an isometry of a symmetric bilinear pairing, the elementary identity (B^i v,B^j v)=(v,B^{j-i}v), together with symmetry, reduces the claim to (v,v)=-2, (v,Bv)=-3 when n>=2, and (v,B^k v)=-4 for every 2<=k<=n-1. These are the exact remaining numerical obligations; none is verified by the packet."
    },
    {
      "kind": "map_correction",
      "source_quote": "\\begin{corol}\\label{corol form 1}",
      "explanation": "The frozen map supplies no dependencies, and the source slice consists only of the corollary statement. Any intended preceding proposition or computation must be located before its inference can be assessed. The absent anchor should not be classified as a manuscript proof error."
    }
  ],
  "dependency_proposals": [
    {
      "label": "Definitions of the family, orbit vector, and normalized form",
      "role": "proof_input",
      "source_quote": "Let $(\n\\cdot,\\cdot)$ be the normalized quadratic form preserved by $\\mathcal{N}_1(1,n,n)$.",
      "explanation": "These internal definitions are necessary to make the asserted numerical pairings checkable. Their location and contents are not supplied."
    },
    {
      "label": "Preceding orbit-pairing computation, if intended",
      "role": "unclassified",
      "source_quote": "If $1 \\le i,j \\le n$ then $$(B^iv,B^jv)=",
      "explanation": "A result computing the pairings of v with its B-orbit could justify the corollary after the elementary isometry reduction. The packet does not identify such a result, so its existence or applicability is not assumed."
    }
  ],
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      "schema": 1,
      "cutoff_date": "2013-08-11",
      "basis": "journal_received",
      "evidence": "Publisher PDF p.1617 states Received August 11, 2013; publisher.html independently records Submitted 11 August 2013. Reviewed native source is arXiv v2 dated 2013-08-12; that does not advance the external proof-input cutoff. ArXiv v1 is 2013-05-03. Later sources may provide retrospective context, not proof inputs for the original paper.",
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