{
  "subject": "Graffiti 292 candidate proof package",
  "statement_source": {
    "title": "Written on the Wall",
    "page": 80,
    "local_file": "wow-july2004.pdf",
    "ocr_file": "page80-detail.txt",
    "statement": "If girth is at least 5 then the minimum positive adjacency eigenvalue is at most n / mean gravity."
  },
  "claims": [
    {
      "id": "C1",
      "claim": "mean(Gr) <= 4m^2/(n^2(n-1))",
      "type": "proved",
      "evidence": "manuscript-graffiti-292.md, Lemma 1"
    },
    {
      "id": "C2",
      "claim": "every adjacency eigenvalue has absolute value <= sqrt(2m)",
      "type": "proved",
      "evidence": "trace(A^2)=2m; manuscript Lemma 2"
    },
    {
      "id": "C3",
      "claim": "C4-free graphs satisfy m <= n(1+sqrt(4n-3))/4",
      "type": "external theorem",
      "evidence": "Jukna, Extremal Combinatorics sample, section 2.2, search result and local citation note"
    },
    {
      "id": "C4",
      "claim": "For n>=7, (n-1)n^3/(4B(n)^2) >= sqrt(2B(n))",
      "type": "symbolically verified",
      "evidence": "verify_symbolic_292.py and verify_symbolic_292_output.txt"
    },
    {
      "id": "C5",
      "claim": "All connected simple girth>=5 graphs of order <=7 satisfy Graffiti 292",
      "type": "exact exhaustive computation",
      "evidence": "verify_small_cases_exact.py and verify_small_cases_exact_output.txt; 35 graph-atlas cases, exact characteristic polynomials and rational root isolation"
    },
    {
      "id": "C6",
      "claim": "Graffiti 292 follows from C1-C5",
      "type": "candidate proof conclusion",
      "evidence": "manuscript-graffiti-292.md"
    }
  ],
  "known_risks": [
    "Historical nomenclature uses OCR-corrupted typography; the page scan should be inspected in publication layout.",
    "A domain expert should independently verify the intended definition of mean gravity and whether the average is over all n^2 entries, as used in the source implementation and prior transcript.",
    "The proof is mathematically complete under the stated normalization, but has not yet received external peer review."
  ]
}