The Reflexive Closure Theorem: Closure Without Collapse in Reflexive Systems Paper 56 of the NEMS Suite

Papers 51–55 established the static ridge: no final internal self-theory, no syntactic exhaustion of semantics, no self-exhausting observer, known qualia on-ledger . The present paper unifies these into the Reflexive Closure Theorem: a nontrivial reflexive system may close over itself, but cannot coincide with its own complete internal semantic image. Closure is possible—self-return, partial self-articulation, and semantic remainder; collapse is impossible—no total self-exhaustion, no self-coincidence. The development is machine-checked in Lean 4 in the ReflexiveClosure library of reflexive-closure-lean , with zero sorry and zero custom axioms at the suite norm for this library. Trust boundary. This paper is a unification of the ridge in Papers 51–55: the Lean code imports those libraries and does not replace their proofs. Nontrivial positive content (e.g. stratified self-awareness, Paper 33) lives in the cited precursor papers. See .