{"id":"hexagon/2610.00388","pdf":"https://hexagonmath.org/pdf/2610.00388v1","url":"https://hexagonmath.org/abs/2610.00388v1","tags":["math.CO","msc:92C42","msc:15A39","msc:05C70","msc:15B48","Lean formalization","autocatalytic networks","boundary traces","child-selection cores","degradation"],"score":0,"title":"Exact interfaces for modular autocatalytic networks","domain":"math.OC","origin":"ai-generated","source":"hexagon","authors":["Michael Mislan"],"reviews":0,"subject":"math.OC","summary":"We study which information about an autocatalytic reaction network suffices for exact composition with other modules. For the maximum amplification factor, threshold-indexed species-price cones compose by exact set operations, while scalar optima do not. Autocatalytic child-selection cores are reconstructed from complete, uniquely matched ordinary-core anchors using alternating exchange paths and certified rational semipositivity tests. For irreducible unary diluted source networks, positive-composition certificates characterize growth, criticality and extinction under arbitrary species…","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withdrawn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-2026-09-25-000027&version=1"],"human_understanding":"some"}