{
  "abstract": "For a positive integer $n$, let $a(n)$ be the largest number of sides of a simple cyclic polygon of circumradius $n$ whose side lengths are positive integers. For primes $p,q$ we show that $a(pq)\\in\\{6,8,18\\}$ and characterize each value by conditions on Gaussian and Eisenstein integers. For every integer $N\\ge2$, on the other hand, $a(N^e)\\to\\infty$ and $\\limsup_{e\\to\\infty}a(N^e)/e\\ge2\\sqrt2$; a quadratic chord tower combined with Farey neighbors gives explicit polygons, for instance $a(8192)\\ge38$. We also show that an odd-sided polygon of radius $n$ exists if and only if $n$ has a prime divisor congruent to $1\\pmod4$, and that $a(n)$ is even whenever at most one distinct prime divisor of $n$ is congruent to $1\\pmod4$; it is also even when the Gaussian part of $n$ is the product of two distinct primes congruent to $1\\pmod4$. Moreover, $a(N^e)=O_N(e^{ω(N)})$ for every fixed $N\\ge2$, and $a(q^e)=Θ(e)$ for primes $q\\equiv1\\pmod4$; exceptional semiprime extremisers have unique side-length multisets. The proofs use a splitting lemma for angle relations by squarefree class, arithmetic in imaginary quadratic fields, bounded zero-sum problems, and a one-dimensional Farey argument. No computer-assisted step is used.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02712",
  "author_total": 1,
  "authors": [
    {
      "name": "Felix Huber"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0691t5w2m3vt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02712",
  "fulltext_url": null,
  "id": "f0691t5w2m3vt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02712",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02712",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0691t5w2m3vt.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02712",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02712"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Semiprime Rigidity and Growth along Powers in Integer-Sided Cyclic Polygons",
  "title_text": "Semiprime Rigidity and Growth along Powers in Integer-Sided Cyclic Polygons",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/f0691t5w2m3vt",
  "venue": "arXiv",
  "versions": []
}