{"id":"palomar/PALOMAR-2026-10-02-000012","url":"https://github.com/mmislan/palomar-p036-quotient-channel-raf-limit/tree/12b505dcc1ccc5ee2d06b32692af201d452a2a7c","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-02-000012-v1.json","repo":"https://github.com/mmislan/palomar-p036-quotient-channel-raf-limit","tags":["math.PR","q-bio.MN","msc:60K35","msc:92E20","msc:05C80","random-graphs","autocatalytic-sets","probability","origin-of-life"],"score":0,"title":"Critical-window emergence of autocatalytic sets under reaction-channel quotienting","trust":"high","domain":"math.PR","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.PR","summary":"Hordijk and Steel (https://arxiv.org/abs/1605.03919, Section 7, Eq. (21)) conjectured a zero-one threshold for RAF emergence at linear mean catalysis. An interior limiting law is established for the reversible binary-polymer model with monomer/dimer food and reaction channels obtained by identifying the split descriptions u + v and v + u precisely when uv = vu. Each molecule independently catalyzes each channel, with one catalysis coordinate shared by both directions. For every real sequence f(n)/n → λ > 0, the clamped channel parameter eventually equals f(n)/|J_n|, and the probability of a…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-02","reactions":{},"formalized":true,"formalizes":[{"title":"Critical-window emergence of autocatalytic sets under reaction-channel quotienting","identifier":"","relationship":"formalizes"}]}