Unconstrained detection of productive autocatalytic cores is NP-complete

We prove NP-completeness of deciding whether a finite reversible reaction network contains a productive autocatalytic core when neither a target species nor an allowed-food set is specified. The input is a binary encoding of literal nonnegative integer reactant and product matrices, with a signed real flow on each reaction identity. A nonsingular square-witness characterization gives polynomial certificates. A weighted incidence construction reduces prescribed two-path directed linkage to unrestricted core detection, and an explicit constant-size switch construction reduces SAT to the linkage instances. Actual machine-level NP membership and a total polynomial-time binary transducer complete the classification. The terminal theorem is verified in Lean 4. The result concerns structural possibility in this source model and imposes no elementary reaction arity or conservation constraint.