Same-ground RAF realizability of finite interior operators and the four-reaction threshold for the empty-or-at-least-three family
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…
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