bibkey: jeandel2026sse
authors: Emmanuel Jeandel
year: 2026
title: Combinatorial Search for Strong Shift Equivalence
doi: null
url: https://arxiv.org/abs/2609.03567v1
claim: The archived v1 TeX source asks whether the Baker polynomial pair is strong shift equivalent over the semiring of polynomials with nonnegative integer coefficients; the question is after the rendered document ends.
strata_touched: []
license: citation-only
triage: anchor

Baker polynomial draft question

The archived source SSE.tex, lines 731-738, asks whether the matrices with rows (1,t+1),(t,1) and (1,t^2+t),(1,1) are strong shift equivalent over the semiring of polynomials with nonnegative integer coefficients. The rendered document ends at line 628. This is an externally authored archived draft question, not a rendered or numbered published problem. The source SHA-256 is a8cdbd3f4181bd10402710aa28c2b71c2e4dd88978eaee0c0ad257f50572b4da.

BakerPolynomialObstruction.no_lag excludes every natural lag for this literal pair over Polynomial Nat. Its no_exchange_chain consequence uses the existing rectangular chain-to-lag theorem and allows arbitrary finite intermediate dimensions. The proof combines the irreducibility of 1-X-X^2 over the rationals, determinant-degree parity, and coefficientwise noncancellation. The irreducibility input is reused from the repository’s multinacci theorem at order two; the degree obstruction is the substantive argument for this pair.

This attribution concerns the question’s source. It makes no claim that the argument is the author’s, that no earlier proof exists in the full literature, that this is a unique solution, or that it settles the general integer-evaluated Baker problem. Real-coefficient polynomial rings are outside the formal statement.

Verified locator

Primary record: https://arxiv.org/abs/2609.03567v1. Archived source: https://arxiv.org/src/2609.03567v1, member SSE.tex, question lines 731-738; end of rendered document at line 628.