{"id":"hexagon/2610.00389","pdf":"https://hexagonmath.org/pdf/2610.00389v1","url":"https://hexagonmath.org/abs/2610.00389v1","tags":["math.CO","msc:60C05","msc:05C65","Lean formalization","RAF sets","binary polymer model","minimum RAF size","probabilistic combinatorics","sparse catalysis"],"score":0,"title":"Linear-size autocatalytic sets are asymptotically absent in the sparse binary polymer model","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["Michael Mislan"],"reviews":0,"subject":"math.PR","summary":"In the sparse binary polymer model with reversible ligation and cleavage, we prove that for every fixed food horizon, fixed nonnegative catalysis intensity and fixed linear reaction budget, the probability of a nonempty reflexively autocatalytic and food-generated set within that budget tends to zero, at rate O(1/n). The probability that a single molecule catalyses a self-constructing reaction set also vanishes, cleavage included. A productive-prefix argument excludes bounded catalyst counts, while an injective acyclic dependency encoding supplies a factorial saving in the count of…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-09-25-000021&version=1"],"human_understanding":"some"}