Closure Is Not Erasure: A Minimal-State Theory of History-Sensitive Recovery and the Evidential Boundary of Experand

Abstract

Restored competence does not establish that a disturbance has been erased. A system may close an unresolved condition yet retain a causally effective distinction between histories that now share endpoint status and report. Motivated by Recovery Without Reset in the Experand adequacy framework, this paper applies classical future-equivalence minimization to independently certified closure cohorts, deriving the minimum complete-state capacity required to preserve their distinguishable continuations. For finite observations with jointly certified uncertainty sets, an incompatibility graph supplies a conservative state bound, with a directly verifiable clique certificate. We distinguish the broad condition of a post-closure historical difference from the stronger case in which the histories are observationally identical at closure and diverge only under a later probe. Finite constructions separate this delayed-revelation property from possibility ordering and noncommutative composition; a geometric example shows why independent causal variables need not admit global fixed-direction neural edits. A retrospective calculation using an archived event log and five recurrent networks illustrates the finite bound, but the order-dependent score was a supervised target and already separated the histories at closure. Its NOP continuation therefore does not demonstrate delayed revelation or a novel recovery mechanism. The account specifies the causal-state obligations supported by operational evidence while leaving phenomenal ownership and intrinsic valence to Experand’s constitutive theory.