{
  "schema_version": 1,
  "problem_number": "AIM-COMPUTATION-0052",
  "title": "An Explicit Nullstellensatz Certificate for the Seventh Hadamard Ideal",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "The nonexistence of a Hadamard matrix of order 28 with one circulant core is classical. A separate AIM workshop challenge asks for an explicit polynomial combination of the 41 generators of the seventh Hadamard ideal that equals one. We give this combination over the rationals in factored finite-sum form, with total degree at most 29. Compression from length 27 to length 9 leaves 36 compressed rows and 78732 Boolean lifts. Boolean projectors and ordered polynomial differences convert the exhaustive finite computation into explicit multipliers for the original generators, using 340840 leaf identities. The package includes integer enumeration, exact symbolic identity checks and a separate bit-mask replay. The contribution is the explicit reproducible certificate, not a new Hadamard nonexistence theorem, a new general Nullstellensatz method or a claim of optimal degree. The other workshop questions concatenated in AIM-COMPUTATION-0052, including the contingency-table cell-spectrum question, are not resolved. This is a self-audited, AI-assisted, unrefereed preprint.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.AC",
    "math.CO"
  ],
  "keywords": [
    "Hadamard ideal",
    "Nullstellensatz certificate",
    "circulant core",
    "Boolean projectors",
    "polynomial identity",
    "AIM-COMPUTATION-0052"
  ],
  "manuscript_version_date": "2026-10-19",
  "publication_date": "2026-10-19",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-19",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-computation-0052/",
  "pdf_url": "https://eulersolve.org/papers/aim-computation-0052/paper.pdf?v=ce9710ccb17d",
  "doi": "10.5281/zenodo.23459784",
  "zenodo_record_url": "https://zenodo.org/records/23459784",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Explicit rational certificate for the canonical 41-generator seventh Hadamard ideal, of degree at most 29. The Hadamard nonexistence theorem and general certificate techniques are classical. The other questions merged in AIM-COMPUTATION-0052, including the contingency-table cell-spectrum question, remain unresolved. Self-audited, AI-assisted and unrefereed; no independent review, formal verification, optimality or absolute-priority claim.",
  "files": {
    "paper.pdf": {
      "sha256": "ce9710ccb17da68b3e5c01108d697c9ab8f67667f177dd495d6f0d42045e9d8a"
    },
    "source.zip": {
      "sha256": "0c5e60fbeb7c543d03aae19584f5001f5be00fdf08f143e1133204d10ca400c0"
    },
    "verification_report.md": {
      "sha256": "4b0eb4120d2f80c27b05f17fa32c38538622b3c54274772ed822226799b95be6"
    }
  },
  "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."
}