{"id":"palomar/PALOMAR-2026-09-25-000021","url":"https://github.com/mmislan/palomar-p012-sparse-raf-exclusion/tree/324c7903021c54c3ee140637a98aef8766ec348b","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-25-000021-v1.json","repo":"https://github.com/mmislan/palomar-p012-sparse-raf-exclusion","tags":["math.PR","msc:60C05","msc:05C65","probability","autocatalytic-sets","random-graphs","reaction-networks"],"score":0,"title":"Linear-size autocatalytic sets are asymptotically absent in the sparse binary polymer model","trust":"high","domain":"math.PR","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.PR","summary":"In the sparse binary-polymer model with reversible ligation and cleavage, fix the food-length bound t, a nonnegative catalysis intensity lambda, and a linear reaction budget Cn. As the maximum polymer length n tends to infinity, the probability of a nonempty reflexively autocatalytic and food-generated reaction set with at most Cn channels tends to zero. The probability that some molecule catalyses a nonempty food-generated reaction set that constructs that molecule also tends to zero. These statements address the linear-size and single-molecule self-construction questions for the sparse…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true,"formalizes":[{"title":"Linear-size autocatalytic sets are asymptotically absent in the sparse binary polymer model","identifier":"","relationship":"formalizes"}]}