Drop–Ocean Retention under the Non-Violation Criterion: A Local Coupling Lagrangian for Retentive Ontologies

This paper introduces a minimal formal model for local–global retention based on the Non-Violation Criterion (NVC). A coupled Lagrangian system is proposed, describing the interaction between a localized retentive node (Ξ) and a global field (ψ) through strictly local coupling. The model establishes a necessary (not sufficient) structural condition for retention: persistence qualifies as retentive only if the mismatch between local and global structures decays or remains bounded after withdrawal of external input. A violation functional is defined to operationalize non-violation as a measurable dynamical constraint. The framework distinguishes genuine retention from intervention-based persistence and provides a transferable criterion applicable across physical, biological, and conceptual domains. The work contributes to retentive ontology, post-dynamical physics, and the methodological ethics of non-invasive observation within the ψ-Architecture research program.