{
  "schema_version": 1,
  "problem_number": "AIM-COMPUTATION-0020",
  "title": "Sharp Ambiguity Bounds for Surviving Conditional Odds Ratios",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "Fix the support of a binary d-way probability table, its feasible interior one-way margins, and every conditional pairwise odds ratio whose four cells remain positive. The largest possible dimension of the resulting family is ceil(2^(d+1)/3)-d-1 for d >= 2, even with uniform margins. For d >= 3, equality holds precisely on classical extremal square-free layer sets, up to cube automorphisms. These extremizers have no surviving ratios. We also give a four-variable uniform-margin family of dimension five with one genuinely surviving ratio. The proof combines classical mixed coordinates with a pivot-deletion lemma and the Kostochka-Johnson-Entringer vertex theorem. Two exact implementations verify all 65,805 nonempty supports through dimension four. This does not classify arbitrary collapsed marginal ratios or resolve the broad AIM specification question; priority is undetermined.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.ST",
    "math.CO"
  ],
  "keywords": [
    "conditional odds ratios",
    "structural zeros",
    "contingency tables",
    "hypercube",
    "mixed coordinates",
    "AIM-COMPUTATION-0020",
    "math.ST",
    "math.CO"
  ],
  "manuscript_version_date": "2026-10-04",
  "publication_date": "2026-10-04",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-04",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-computation-0020/",
  "pdf_url": "https://eulersolve.org/papers/aim-computation-0020/paper.pdf?v=d0bc25559e6c",
  "doi": "10.5281/zenodo.23130679",
  "zenodo_record_url": "https://zenodo.org/records/23130679",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete proof of the stated binary conditional-ratio extremal theorem, including uniform margins and the equality supports. Classical mixed-coordinate theory, the cube theorem and the structural-zero work of Fontana, Perrone and Rapallo are credited. The broad AIM-COMPUTATION-0020 Question 6, especially arbitrary collapsed marginal odds-ratio specifications, remains unresolved and is not counted as a source closure. Novelty of the statistical transfer is undetermined; no absolute-priority claim. AI-assisted, self-audited and unrefereed; no independent human review or proof-assistant verification is claimed.",
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      "sha256": "d0bc25559e6cc97c23a57e12454c57404d9fccbe7e3feb5555ff3705a1e41265"
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    "source.zip": {
      "sha256": "b6506f221b5bc2323fa80af653198de6e835d06561229319fd9fde6cd14ba854"
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    "verification_report.md": {
      "sha256": "d821b682d2ea6b0a1c5fbc88848e2e618367117ab12ad8629fb5a4f580a5213f"
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  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}