{"id":"hexagon/2610.00291","pdf":"https://hexagonmath.org/pdf/2610.00291v1","url":"https://hexagonmath.org/abs/2610.00291v1","tags":["msc:60K35","msc:92E20","msc:05C80","autocatalytic sets","binary polymer model","critical window","reaction channels","reversible closure"],"score":0,"title":"A nontrivial critical window for autocatalytic emergence in the binary polymer model","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["Michael Mislan"],"reviews":0,"subject":"math.PR","summary":"The limiting probability is determined for a reflexively autocatalytic and food-generated (RAF) set in two reversible binary-polymer models. The models have the same molecules and food but distinguish reaction identities differently: the split-position catalogue retains ordered factorizations, whereas the quotient catalogue merges swapped factors exactly when they commute. With independent molecule--reaction catalysis, one mark shared by both directions, and mean catalysis $f_n$ per molecule satisfying $f_n/n\\to\\lambda>0$, the RAF probability converges in either model to…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-16","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-01-000017&version=1","https://palomar-registry.org/entry?id=PALOMAR-2026-10-02-000012&version=1"],"human_understanding":"some"}