{
  "target_id": "corol form 3",
  "proof_status": "needs_context",
  "summary": "The packet supplies the corollary but neither its computational inputs nor definitions of the family, B, v, and the normalization. Conditional on B preserving the form, the claimed entries reduce to finitely many scalar products, but their numerical values cannot be checked from this packet. The missing proof anchor is a mapping limitation, not evidence of a manuscript proof defect. No external result is imported.",
  "used_dependencies": [],
  "missing_context": [
    "Definition of \\mathcal{N}_1(3,n,n), including all dimension and parameter restrictions.",
    "The family-specific matrix B and vector v, including their coordinate conventions.",
    "Definition and normalization of the preserved symmetric form, and identification of B as an isometry of it.",
    "The preceding result or calculation establishing the required scalar products, together with the intended proof anchor for this corollary."
  ],
  "findings": [
    {
      "kind": "context",
      "source_quote": "be the normalized quadratic form preserved by $\\mathcal{N}_1(3,n,n)$.",
      "explanation": "The supplied excerpts do not define this family, its admissible parameters, or the normalization. The introduction defines a general monodromy matrix B, but does not specialize it to this family or define v. Consequently, neither preservation by this particular B nor the scale producing diagonal entries -2 can be checked."
    },
    {
      "kind": "unverified",
      "source_quote": "$$(B^iv,B^jv)=\\left\\{\\begin{array}{ccc}",
      "explanation": "If B preserves the symmetric form, then for j>=i one has (B^iv,B^jv)=(v,B^{j-i}v); symmetry handles j<i. Thus the exact remaining numerical obligation is to establish the moments for d=0,...,n-1: -2 at d=0, -4 at d=1, -8 at d=2 or n-1, -11 at d=3 or n-2, and -12 at every remaining distance. No matrix, recurrence, coefficient formula, or preceding calculation establishing these moments is supplied."
    },
    {
      "kind": "context",
      "source_quote": "If $1 \\le i,j \\le n$ then",
      "explanation": "An admissible range for n must be inherited from the omitted family definition. For n>=5 the cases are disjoint and exhaust the possible distances. At n=3, distance 1 satisfies both the -4 condition and the -11 condition; at n=4, distance 2 satisfies both the -8 and -11 conditions. These are conditional inconsistencies, not established errors, because the omitted definition may exclude these dimensions."
    },
    {
      "kind": "map_correction",
      "source_quote": "\\begin{corol}\\label{corol form 3}",
      "explanation": "The supplied scope contains only the statement, with no proof or dependency edges. A preceding calculation or definition may supply the justification. Its absence from the packet should be recorded as missing mapping context rather than attributed to the manuscript as a missing proof."
    }
  ],
  "dependency_proposals": [
    {
      "label": "Family definition and admissible dimensions",
      "role": "proof_input",
      "source_quote": "$\\mathcal{N}_1(3,n,n)$",
      "explanation": "Locate the definition to determine which n are permitted and how the named family supplies B and v. This is a proposed missing input, not an established dependency."
    },
    {
      "label": "Preserved-form normalization",
      "role": "proof_input",
      "source_quote": "the normalized quadratic form",
      "explanation": "The normalization must specify the scale and justify the asserted norm of v; preservation alone does not determine the displayed numbers."
    },
    {
      "label": "Family-specific scalar-product calculation",
      "role": "proof_input",
      "source_quote": "(B^iv,B^jv)",
      "explanation": "Locate a computation of (v,B^d v), or equivalent explicit matrix data from which these values follow. No theorem label or proof anchor for that computation is supplied."
    }
  ],
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    "custom_id": "claim-ee227ab9554356d1802189bc",
    "source_sha256": "cb1785e680f92da29e933d6bada70f9e116c07938eabbad8ab76a67dac6ac98b",
    "usage": {
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      "output_tokens_details": {
        "reasoning_tokens": 1032
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    "max_output_tokens": 24576,
    "prompt_profile": "claim_review-v2",
    "prompt_profile_sha256": "600c451625bbe1d6d19828dfd9fb687fea4ac45fe9189b2bf52bc25ef9e1edcb",
    "review_policy": {
      "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.",
      "status": "recorded",
      "rule": "external-results-available-by-cutoff"
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}