Programme status: This record belongs to an active research programme. It is not a finished or final theory. The framework is currently undergoing a systematic audit, together with corrections and improvements prompted by reader feedback. Several significant issues have been identified, and some claims, derivations and interpretations in the current version may be revised, qualified or withdrawn in future versions. Revised versions will be released when this work is complete. Status as of October 2026. We adopt a strong locality axiom at the Holds level: factorization—global satisfaction of observational propositions is the conjunction over fragments of a local predicate applied to the restricted world. This is algebraic, not geometric; no spacetime structure is assumed. Under factorization, same local views (same restriction at every fragment) imply observational equivalence; hence world-type is determined by the global map from fragments to local views. Interpretation: local dynamics alone do not guarantee local semantic closure; semantics is glued globally. A minimal toy (two fragments, observables as per-fragment claims) witnesses factorization and the main theorem. The development is mechanized in Lean 4 as the SemanticNonlocality library in nems-lean, with zero sorry and no custom axioms. Trust boundary. Factorization is an algebraic \Holds-level axiom, not a spacetime locality claim; interpretive "nonlocality" language is about semantic gluing, not signalling. Mechanization is nems-lean . See .