Arithmetic Primitive-Orbit Rigidity in Stationary CCR Polynomials: Shift Companions, Prime Divisors, and Bernoulli Ladders
- 1Independent Researcher
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.
Related
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BibTeX
@misc{butun2026arithmetic,
title = {{Arithmetic Primitive-Orbit Rigidity in Stationary CCR Polynomials: Shift Companions, Prime Divisors, and Bernoulli Ladders}},
author = {Alp Eren Bütün},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23670946},
url = {https://zenodo.org/records/23670946},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Arithmetic Primitive-Orbit Rigidity in Stationary CCR Polynomials: Shift Companions, Prime Divisors, and Bernoulli Ladders
AU - Alp Eren Bütün
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23670946
UR - https://zenodo.org/records/23670946
AB - 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.
ER -