{
  "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"
  },
  "proof_inputs": [
    {
      "key": "nik",
      "role": "proof_input",
      "available_from": "1979",
      "date_evidence": "Original Doklady 248(6) (1979), pp.1307\u20131309; MathNet dan43091 bibliographic record; scanned article text contains Theorems 1,4,5.",
      "date_basis": "original_journal_publication",
      "version": "1979 original Russian journal article",
      "imported_result": "Even hyperbolic 2-reflective lattice classification, Theorems 1,4,5; <-16>+D4 is reflective after reversing sign.",
      "required_hypotheses": "Integral even nondegenerate hyperbolic lattice, rank >=5; exact integral isomorphism or invariant exclusion, with 2-elementary cases retained separately.",
      "source_url": "https://www.mathnet.ru/eng/dan43091",
      "cache": "nikulin-1979-web-extract.txt",
      "original_pdf_locally_archived": false,
      "audit_scope": "The theorem statement and application hypotheses, not a reproof of the classification.",
      "cache_sha256": "ee6b4b7786c969ad2b6469847f477b8e7e2db344f05221923729c0851f13e2da"
    },
    {
      "key": "bh",
      "role": "proof_input",
      "available_from": "1989",
      "date_evidence": "Original Inventiones Mathematicae 95 (1989), pp.325\u2013354, visible in cached published PDF.",
      "date_basis": "original_journal_publication",
      "version": "1989 published paper",
      "imported_result": "Theorems 3.5,5.8,6.5: companion realization, imprimitivity criterion, orthogonal Zariski closure.",
      "required_hypotheses": "Disjoint nonzero spectra; irreducible reflection subgroup; primitive infinite hypergeometric group not a scalar shift of a finite group; reciprocal spectra; c=-1.",
      "source_url": "https://math.uchicago.edu/~drinfeld/Hypergeometric_motives/Beukers-Heckman.pdf",
      "cache": "beukers-heckman-1989.pdf",
      "audit_scope": "Stated classical inputs and application hypotheses; classical proofs not re-audited.",
      "cache_sha256": "b967ed4369ada16ec9ff6d0d828f9984d8de7dbf1591c71562c7c44ce272ebda"
    }
  ],
  "background_only": [
    "nikulin-2008-v1.pdf"
  ],
  "not_required": [
    "Vinberg high-dimensional nonreflectivity theorem"
  ]
}