{"id":"palomar/PALOMAR-2026-09-30-000011","url":"https://github.com/mmislan/palomar-p082-acr-zero-divisors/tree/a2bcfab8f3015df957bc20da1db66cbf1ae98bd0","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-30-000011-v1.json","repo":"https://github.com/mmislan/palomar-p082-acr-zero-divisors","tags":["math.AC","q-bio.MN","msc:13P10","msc:13P25","msc:92C42","reaction-networks","commutative-algebra","concentration-robustness"],"score":0,"title":"Zero-divisor criteria for absolute concentration robustness","trust":"high","domain":"math.AC","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.AC","summary":"García Puente et al. (arXiv:2401.00078v3, Question 3.13) asked whether a unique positive zero-divisor value is necessary or sufficient for absolute concentration robustness (ACR) in at-most-bimolecular mass-action networks. Explicit networks with positive rational rates answer both questions negatively. A further three-species example shows that their candidate algorithm can miss a zero-divisor ACR value under an admissible elimination order, refuting the unrestricted elimination-order form of Conjecture 4.7. For block orders that compare the other species before the distinguished species,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-30","reactions":{},"formalized":true,"formalizes":[{"title":"Zero-divisor methods for absolute concentration robustness: completeness, positive geometry, and quantitative certificates","identifier":"","relationship":"formalizes"}]}