{
  "abstract": "The paper develops the reverse prime-to-CCR direction of our arithmetic transport research, asking when the Nörlund–Stirling shadow of a later stationary CCR column contains a genuinely new irreducible factor or root orbit not inherited from earlier columns. It establishes exact trailing-source interpolation limits and a shift-companion identity that reduces adjacent-column common factors to a self-translation gcd, yielding structural degree obstructions. It then proves source-independent nonsharing for several families of sufficiently long Frobenius orbits. Using a classical large-Zsigmondy-prime theorem together with new exact polynomial arguments, it establishes rational predecessor-factor noncoverage at every odd order, and derives cofinite good-prime and positive-density primitive-root consequences at fixed order. An explicit coefficient-content criterion decides exceptional good primes order by order; exact finite certificates establish polynomial noncoverage at every good prime for odd orders through 71. Bernoulli-coordinate ladders and primitive p-adic root examples complete the picture. Its main novelty is a unified arithmetic theory of source-uniform primitive-orbit rigidity and effective predecessor noncoverage. The stronger all-order, every-good-prime assertion remains open, and no physical automaton-realizability theorem is claimed.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Alp Eren Bütün",
      "orcid": "0009-0001-2479-6037"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4s91hrwdjnqnb.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23670946",
  "fulltext_url": null,
  "id": "4s91hrwdjnqnb",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23670946",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23670946/files/Arithmetic_Primitive_Orbit_Rigidity_in_Stationary_CCR.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4s91hrwdjnqnb.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:20:47Z",
      "native_id": "23670946",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23670946"
    }
  ],
  "subjects": [],
  "title": "Arithmetic Primitive-Orbit Rigidity in Stationary CCR Polynomials: Shift Companions, Prime Divisors, and Bernoulli Ladders",
  "title_text": "Arithmetic Primitive-Orbit Rigidity in Stationary CCR Polynomials: Shift Companions, Prime Divisors, and Bernoulli Ladders",
  "type": "preprint",
  "updated_at": "2026-11-09T12:20:47Z",
  "url": "https://research.draconitic.com/paper/4s91hrwdjnqnb",
  "venue": "Zenodo",
  "versions": []
}