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  "slug": "essential-hurwitz-trace-formula",
  "title": "A ten-by-ten trace formula for the essential Hurwitz form",
  "shortTitle": "A small trace matrix for the Hurwitz form",
  "url": "https://evidencepress.org/releases/essential-hurwitz-trace-formula/",
  "oneLine": "A compact trace-determinant formula candidate gives the global degree-30 essential Hurwitz form, with a denominator-cancellation proof and symmetric corollary.",
  "abstract": "This unrefereed candidate gives H=D^4 det(T), using the trace pairing of a rank-ten quotient algebra. The written proof identifies the sole possible Chow-boundary denominator, proves global cancellation and identifies the degree-30 Pluecker Hurwitz divisor with multiplicity one. Exact rational evaluation includes chart conversion and a finite boundary fallback. The same argument yields the symmetric rank-two four-by-four corollary. Classical trace-discriminant antecedents and earlier specialized computations are credited. The result is a compact arithmetic formula, not an expanded monomial list or a measured camera-estimation improvement.",
  "datePublished": "2026-09-07",
  "dateModified": "2026-09-07",
  "version": "0.1.0-candidate",
  "doi": "10.5281/zenodo.22650445",
  "doiUrl": "https://doi.org/10.5281/zenodo.22650445",
  "conceptDoi": "10.5281/zenodo.22650444",
  "pdfUrl": "https://github.com/ipitchford/essential-hurwitz-trace-formula/releases/download/v0.1.0-candidate/paper.pdf",
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  "authors": [
    "Anonymous"
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  "status": "unrefereed-candidate",
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  "problem": {
    "name": "3264 Questions, Question 20: an explicit essential Hurwitz form",
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  "keywords": [
    "Hurwitz form",
    "essential variety",
    "trace discriminant",
    "algebraic geometry",
    "symmetric matrices"
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  "keyResults": [
    "Ten-by-ten trace formula with a uniform rank-ten algebra.",
    "Global Chow-boundary denominator cancellation and degree-30 Pluecker identification.",
    "Exact boundary interpolation and coordinate interfaces.",
    "Symmetric rank-two corollary and published-fixture controls."
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    {
      "citation": "Sturmfels, The Hurwitz Form of a Projective Variety (2017), Theorem 1.1.",
      "url": "https://arxiv.org/abs/1410.6703",
      "doi": "10.48550/arXiv.1410.6703"
    },
    {
      "citation": "Floystad, Kileel and Ottaviani, The Chow Form of the Essential Variety in Computer Vision (2018), section 2.",
      "url": "https://arxiv.org/abs/1604.04372",
      "doi": "10.48550/arXiv.1604.04372"
    },
    {
      "citation": "Jiang and Sturmfels, Bad projections of the PSD cone (2021), Example 12.",
      "url": "https://doi.org/10.1007/s13348-021-00319-4",
      "doi": "10.1007/s13348-021-00319-4"
    },
    {
      "citation": "D Andrea and Jeronimo, Rational Formulas for Traces in Zero-Dimensional Algebras (2008).",
      "url": "https://doi.org/10.1007/s00200-008-0085-x",
      "doi": "10.1007/s00200-008-0085-x"
    },
    {
      "citation": "Fan, Kileel and Kimia (2025), arXiv:2310.02719v2, Theorem 22 and Remark 23.",
      "url": "https://arxiv.org/html/2310.02719v2",
      "doi": null
    }
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