{"id":"hexagon/2610.00441","pdf":"https://hexagonmath.org/pdf/2610.00441v1","url":"https://hexagonmath.org/abs/2610.00441v1","tags":["math.DS","msc:13P10","msc:13P25","msc:92C42","Lean formalization","absolute concentration robustness","elimination orders","quantitative certificates","steady-state ideals","zero divisors"],"score":0,"title":"Zero-divisor methods for absolute concentration robustness","domain":"math.AC","origin":"ai-generated","source":"hexagon","authors":["Michael Mislan"],"reviews":0,"subject":"math.AC","summary":"We study the relation between absolute concentration robustness and zero divisors in steady-state coordinate rings. Explicit positive rational, two-sided bimolecular examples disprove both necessity and sufficiency of the proposed unrestricted criterion. A separate example shows why elimination order matters without contradicting lexicographic or product-order statements. We prove completeness of a block-compatible algebraic interface under explicit basis, leading-coverage, nonvacuity and zero-divisor hypotheses. The manuscript develops complementary criteria from regular positive geometry…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-21","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-09-30-000011&version=1"],"human_understanding":"some"}