{"id":"palomar/PALOMAR-2026-09-25-000025","url":"https://github.com/mmislan/palomar-p005-raf-interior-realizability/tree/ebc29d42debba48f8ffc90624d7bd14cdb4a281e","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-25-000025-v1.json","repo":"https://github.com/mmislan/palomar-p005-raf-interior-realizability","tags":["math.CO","msc:05B35","msc:05C20","autocatalytic-sets","interior-operators","combinatorics","reaction-networks"],"score":0,"title":"Same-ground RAF realizability of finite interior operators and the four-reaction threshold for the empty-or-at-least-three family","trust":"high","domain":"math.CO","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.CO","summary":"Addressing the RAF-realizability question in Section 4 of Mike Steel's Interior Operators and Their Relationship to Autocatalytic Networks (arXiv:2305.16714v4, 2023), we characterize which interior operators on the subsets of a finite set E are maxRAF operators of catalytic reaction systems whose reaction set is exactly E. An interior operator is represented by its family of fixed sets, a union-closed family containing the empty set. A same-ground realization is a system with one reaction per element of E, finitely many molecule types, a food set and a catalysis relation; it realizes the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true,"formalizes":[{"title":"Interior operators realizable by autocatalytic networks: an antimatroid characterization","identifier":"","relationship":"formalizes"}]}