Bernoulli Transport Sieves and Finite-Range Integer-Source Triple-Zero Exclusion in Stationary CCR Polynomials
- 1Independent Researcher
Abstract
The paper develops a source-uniform impossibility theorem within our stationary chronological-carry-refinement (CCR) polynomial program. The question is whether any choice of ordinary integer connected-source parameters can make the three lowest coefficients of a polynomial column vanish simultaneously. For every odd order from 5 through 75 and every prime transport parameter exceeding twice that order, the paper proves that divisibility by X^3 is impossible for all integer source vectors. It combines Bernoulli-numerator restrictions on transport primes with source-independent prime-order congruences and explicit finite-ring obstructions for exceptional composite orders. A particularly strong order-65 certificate uses uniform p-adic valuation bounds to eliminate higher sources and a Frobenius-function identity covering all 1,013 relevant low-source monomials. Its main novelty is converting a potentially unrestricted search over source vectors and transport primes into a complete, exact 36-order exclusion theorem, with computational certificates serving the universal algebraic reductions rather than sampled evidence. This is a finite-order impossibility theorem for the formal CCR family, not a proof for all odd orders or arbitrary physical automata.
Related
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BibTeX
@misc{butun2026bernoulli,
title = {{Bernoulli Transport Sieves and Finite-Range Integer-Source Triple-Zero Exclusion in Stationary CCR Polynomials}},
author = {Alp Eren Bütün},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23670863},
url = {https://zenodo.org/records/23670863},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bernoulli Transport Sieves and Finite-Range Integer-Source Triple-Zero Exclusion in Stationary CCR Polynomials
AU - Alp Eren Bütün
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23670863
UR - https://zenodo.org/records/23670863
AB - The paper develops a source-uniform impossibility theorem within our stationary chronological-carry-refinement (CCR) polynomial program. The question is whether any choice of ordinary integer connected-source parameters can make the three lowest coefficients of a polynomial column vanish simultaneously. For every odd order from 5 through 75 and every prime transport parameter exceeding twice that order, the paper proves that divisibility by X^3 is impossible for all integer source vectors. It combines Bernoulli-numerator restrictions on transport primes with source-independent prime-order congruences and explicit finite-ring obstructions for exceptional composite orders. A particularly strong order-65 certificate uses uniform p-adic valuation bounds to eliminate higher sources and a Frobenius-function identity covering all 1,013 relevant low-source monomials. Its main novelty is converting a potentially unrestricted search over source vectors and transport primes into a complete, exact 36-order exclusion theorem, with computational certificates serving the universal algebraic reductions rather than sampled evidence. This is a finite-order impossibility theorem for the formal CCR family, not a proof for all odd orders or arbitrary physical automata.
ER -