{
  "abstract": "Let $Ω=2\\int_0^1(1-t^4)^{-1/2}dt$. We prove that, for every real $ν>2$, there is $Q\\geq2$ such that $q^{-ν}<|Ω-p/q|$ for every integer $p$ and every integer $q\\geq Q$. Consequently $Ω$ is irrational and its irrationality exponent is two. The proof combines elliptic separated-weight interpolation, arithmetic denominator estimates, and an analytic determinant bound on a square complex-multiplication grid. The determinant comparison uses the same selected source columns on both sides. We give the integral-to-lattice normalization, the exact local-coordinate and common-multiplier transport, and the parameter order that makes the two bounds incompatible. The accompanying Lean 4 development proves the endpoint without additional hypotheses. Numbered formal references link the mathematical argument to exact declarations in the complete source distribution; an appendix gives the pinned build environment and the dependency audit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26539",
  "author_total": 1,
  "authors": [
    {
      "name": "Gregory V. Chudnovsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e86b5kc8qepfs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26539",
  "fulltext_url": null,
  "id": "e86b5kc8qepfs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26539",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7223052042",
  "pdf_url": "https://arxiv.org/pdf/2610.26539",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e86b5kc8qepfs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26539",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26539"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The irrationality exponent of the lemniscate period: A determinant proof with a Lean 4 formalization",
  "title_text": "The irrationality exponent of the lemniscate period: A determinant proof with a Lean 4 formalization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/e86b5kc8qepfs",
  "venue": "arXiv",
  "versions": []
}