{"id":"palomar/PALOMAR-2026-10-01-000017","url":"https://github.com/mmislan/palomar-p002-binary-polymer-critical-window/tree/f90984f2b107aad62c6efcceb0d8cb9da0fe62a4","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-01-000017-v1.json","repo":"https://github.com/mmislan/palomar-p002-binary-polymer-critical-window","tags":["math.PR","q-bio.MN","msc:60K35","msc:92E20","msc:05C80","autocatalytic-sets","random-graphs","origin-of-life","probability"],"score":0,"title":"A nontrivial critical window for RAF emergence in the binary polymer model","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. In the uniform reversible binary-polymer model with split-position reaction identities and food consisting of monomers and dimers, a nontrivial limiting law is established. Each molecule independently catalyzes each reaction, with one catalysis coordinate shared by both directions. If the mean catalysis parameter f(n) satisfies f(n)/n → λ > 0, the probability of a reflexively autocatalytic and food-generated (RAF) set converges to L(λ). The…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-01","reactions":{},"formalized":true,"formalizes":[{"title":"A nontrivial critical window for RAF emergence in the binary polymer model","identifier":"","relationship":"formalizes"}]}