{
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  "summary": "The target is an announcement of two invariant-form calculations, not a calculation or proof itself. The supplied excerpts support the general setting of invariant hyperbolic quadratic forms, but do not identify the two cases or supply their forms. No local mathematical error is demonstrated. The reference to Section~\\ref{thinguys} indicates subsequent use, not a proof dependency.",
  "used_dependencies": [
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  "missing_context": [
    "The continuation identifying the two cases and displaying their quadratic forms.",
    "The definitions and generator matrices for those cases, sufficient to check invariance directly.",
    "Any normalization, lattice, integrality or signature claims attached to the displayed forms, together with their stated prerequisites or derivations."
  ],
  "findings": [
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      "kind": "context",
      "source_quote": "We now record the invariant quadratic form for two cases that we consider in Section~\\ref{thinguys}.",
      "explanation": "The bounded source contains neither the identities of the two cases nor their proposed quadratic forms. Consequently, their invariance, normalization, integrality and signatures cannot be checked here. This is a packet-scope limitation, not evidence of a manuscript proof defect."
    },
    {
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      "source_quote": "two cases that we consider in Section~\\ref{thinguys}",
      "explanation": "This is a forward application reference. The supplied edge from thinguys to this target should not be treated as establishing the announced forms. The supplied portion of thinguys gives general setup but no case-specific invariant-form calculation."
    },
    {
      "kind": "unverified",
      "source_quote": "Moreover, there is an integer quadratic form $(u_1,u_2)={u_1}^tfu_2$ of signature $(n-1,1)$ preserved by $H$.",
      "explanation": "This supplied dependency asserts general existence of an invariant form. Even if accepted conditionally, it does not identify or verify the two explicit forms announced by the target."
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  "dependency_proposals": [
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      "label": "thinguys",
      "role": "background",
      "source_quote": "We now record the invariant quadratic form for two cases that we consider in Section~\\ref{thinguys}.",
      "explanation": "Retain this as contextual evidence of intended later application, rather than as a proof input for the forms. No external result has been imported in this assessment."
    }
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