{
  "schema_version": 1,
  "problem_number": "AMR-005-0008",
  "title": "Explicit Rotation and Arithmetic Obstructions for Null Chains on a Lorentz Ellipsoid",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "For the ellipsoid x^2/a + y^2/b + z^2/c = 1 in Minkowski space, we compute the positive unreduced rotation lift of the equator return map formed by alternating null geodesics. Put A = 2 integral from 0 to pi/2 of sqrt((a sin^2(t) + b cos^2(t))/(c + a sin^2(t) + b cos^2(t))) dt. A global conformal cylinder and a complementary-period identity give rho = (pi/A - 1)/2. Closure after k equator iterations and r turns is equivalent to A = pi*k/(k + 2*r). Literal tropic-to-tropic chains additionally require an even number of legs. For fixed a,b and a positive target rotation there is exactly one c, with explicit bounds. If a,b,c are positive algebraic numbers with a != b, an application of Wustholz's analytic subgroup theorem to a twice-punctured elliptic curve proves that rho is transcendental, so no chain closes. For a=b, closure is equivalent to sqrt(1+c/a) being rational. Fixed positive rational-rotation loci on a>b>0 are not semialgebraic over the real algebraic numbers and are Zariski dense over the algebraic numbers. GKT's porism, classical generalized-Jacobian theory, Huber-Wustholz and Wustholz's earlier arithmetic announcement are credited. This is an unrefereed, self-audited preprint; no absolute priority or independent or formal verification is claimed.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.DG",
    "math.DS",
    "math.NT"
  ],
  "keywords": [
    "Lorentz ellipsoid",
    "null geodesics",
    "rotation number",
    "generalized Jacobian",
    "analytic subgroup theorem",
    "transcendental periods",
    "AMR-005-0008"
  ],
  "manuscript_version_date": "2026-10-14",
  "publication_date": "2026-10-14",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-14",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/amr-005-0008/",
  "pdf_url": "https://eulersolve.org/papers/amr-005-0008/paper.pdf?v=d4df90f5d14c",
  "doi": "10.5281/zenodo.23371160",
  "zenodo_record_url": "https://zenodo.org/records/23371160",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete analytic closure criterion with explicit equator-iteration and even physical-leg conventions. For unequal positive algebraic horizontal parameters the rotation is transcendental; the equal-axis case is handled separately. Nonsemialgebraicity is restricted to real algebraic coefficients. Prior porism and arithmetic announcements are credited; novelty is not certified. Self-audited and unrefereed; no independent or formal verification claim.",
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      "sha256": "d4df90f5d14c9cab745009a9634a379e2b27ce0419e3b52247ce73a070509158"
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    "source.zip": {
      "sha256": "0b09594dca1775e711644e183576e94802bf58278552e2b6fda15e5fe9a360ba"
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    "verification_report.md": {
      "sha256": "88f2e1a4ba5c84629c71b82fcd701f69f2771350f83a0e35119501bec0378e61"
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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."
}