{"id":"palomar/PALOMAR-2026-10-04-000007","url":"https://github.com/mmislan/palomar-p046-critical-window-shape-law/tree/b46f8d0747b6dfb4c00a50d386f3df4f330e861e","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-04-000007-v1.json","repo":"https://github.com/mmislan/palomar-p046-critical-window-shape-law","tags":["math.PR","q-bio.MN","msc:60K35","msc:92E20","msc:05C80","msc:03D78","msc:68V20","random-graphs","autocatalytic-networks","origin-of-life"],"score":0,"title":"Effective approximation and low-intensity flatness of RAF critical-window profiles","trust":"high","domain":"math.PR","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.PR","summary":"The critical-window laws for autocatalytic emergence in reversible binary-polymer networks lead to survival profiles for independent open reaction channels. For both the ordered split-position and commuting-factor quotient models, with all binary words of length at most two as food, explicit total algorithms enclose each survival probability at every rational openness in [0,1] to any prescribed positive rational accuracy. Computable seed lengths and finite-record contraction estimates provide uniform truncation bounds on intervals bounded away from zero. The associated intensity profiles S(1…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-04","reactions":{},"formalized":true,"formalizes":[{"title":"Effective approximation, low-intensity bounds, and finite-size effects for autocatalytic emergence in reversible polymer networks","identifier":"","relationship":"formalizes"}]}