What question did this study set out to answer?

The aim is to explore the constraints of local semantic determinacy under PSC-style closure and diagonal capability.

April 7, 2026Open Access

Causal Nonlocality from Closure: A No-Go for Naive Semantic Locality Under PSC and Diagonal Capability Paper 46 of the NEMS Suite

Key Points

The aim is to explore the constraints of local semantic determinacy under PSC-style closure and diagonal capability.
Mathematical proof of no-go for strong factorization locality with local semantic determinacy.
Utilization of Lean 4 for mechanization to validate results.
Analysis of the implications of the selector-strength barrier.
Proven that total-effective local semantic determinacy cannot coexist with strong factorization locality.
Demonstrated that asserting local views does not imply superluminal signaling.
Results parametric in the fixed-point premise, specifically involving zero axioms.

Abstract

Under PSC-style closure, stable records, and diagonal capability (Papers 27, 29), one cannot simultaneously hold a strong factorization locality axiom (Paper 45) and local semantic determinacy—that world-type is computed from local views in a total-effective way. We prove a no-go: any such procedure would decide an extensional nontrivial predicate on a diagonal-capable domain and thus contradict the selector-strength barrier. So total-effective local semantic determinacy must fail (factorization can hold). This is semantic nonlocality in the effective sense, without implying superluminal signalling. The result is mechanized in Lean 4 (CausalNonlocality); the barrier witness is parametric in the fixed-point premise (0 axioms). Paper 47 (No Spooky-to-Signal Compiler) builds on this. Trust boundary. The no-go combines Paper 45 factorization with a total-effective local semantic determinacy hypothesis; it does not assert superluminal signalling. Mechanization is nems-lean . See .

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