{
  "schema_version": 1,
  "problem_number": "AIM-COMPUTATION-0040",
  "title": "A Connected Positive Model with a Nonsemialgebraic Likelihood Cell",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We give a connected compact rational polygonal model on four outcomes, all of whose probabilities are at least 1/32, with a nonsemialgebraic logarithmic Voronoi cell at a smooth rational point. Near a positive data vector, the cell is the epigraph of an explicit binary entropy expression in rational coordinates. A uniform likelihood gap shows that the connecting segment does not alter this boundary. An elementary proof establishes nonsemialgebraicity over the real numbers. Four outcomes are minimal at a positive-dimensional smooth interior model point, by log-normal containment and convexity. This five-page note complements the earlier work of Alexandr and Heaton and Alexandr's 2026 nonalgebraicity results. It provides a complete explicit theorem relevant to AIM-COMPUTATION-0040, not a full closure of the open-ended AIM Question 26. AI-assisted, self-audited and unrefereed; no formal verification, independent peer review, or absolute priority is claimed.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.ST",
    "math.AG"
  ],
  "keywords": [
    "logarithmic Voronoi cell",
    "maximum likelihood",
    "semialgebraic geometry",
    "binary entropy",
    "connected statistical model",
    "AIM-COMPUTATION-0040"
  ],
  "manuscript_version_date": "2026-10-18",
  "publication_date": "2026-10-18",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-18",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-computation-0040/",
  "pdf_url": "https://eulersolve.org/papers/aim-computation-0040/paper.pdf?v=a72ee27f0291",
  "doi": "10.5281/zenodo.23444649",
  "zenodo_record_url": "https://zenodo.org/records/23444649",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete explicit connected positive four-outcome example, nonsemialgebraic likelihood cell at a smooth rational point, and sharp outcome bound for positive-dimensional smooth interior model points. The model is polygonal, not globally smooth. The broad AIM Question 26 is not closed. Earlier nonalgebraicity work of Alexandr and Heaton and Alexandr is credited. AI-assisted, self-audited and unrefereed; no independent review, formal certification or absolute-priority claim.",
  "files": {
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      "sha256": "a72ee27f0291e5c066f4872f9a866cdcee36e19f5e0bcdcff6a73ad4fa8e80e3"
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    "source.zip": {
      "sha256": "405e79367aa61bf94e8c151dfabcb94cedc0256cbb3b3df8f095537ecb9efd04"
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    "verification_report.md": {
      "sha256": "f884bba215337966cc9b8746500326666ced7bd8b7a3dd22d44f355e6c120079"
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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."
}