Synchronization Mesh Protocol: Synchronization as the Operational Prerequisite for Physical Laws

This paper formalizes "synchronization" as a protocol—the prerequisite condition for the validity of conservation laws, motion, force, and observation. Synchronization is not a new hypothesis but rather an explicit specification of the implicit assumptions underlying existing physics: comparability, consistency recovery, and non-collapse update. We introduce a three-layer model: Protocol Layer (A-layer): Synchronization Mesh (S-mesh) as consistency conditions without velocity concept Implementation Layer (B-layer): S-propagation with finite propagation limit c and update rate Observation Layer (C-layer): Observable quantities including time delay, effective velocity, and gravity The core contribution is the Minimal Axiom Set (P1–P5): P1: Comparability — physical quantities must be comparable within the same system P2: Relaxation — local inconsistencies must be statistically recoverable P3: Non-collapse Update — system-wide updates must not stop or collapse P4: Locality — the protocol is applied locally, not as global simultaneity P5: Fault Isolation — local failures do not collapse the entire system We position the OU correlation time τ_c observed in V112 as the "synchronization relaxation time," providing a framework to treat it as an observable measure of sync quality (stiffness/viscosity). The correlation length ℓ_c = c × τ_c ≈ 0.18 AU emerges as a potentially significant physical scale. Falsifiable predictions include: (P) environmental dependence of τ_c, (Q) physical significance of the correlation length scale, and (R) staged disconnection near black holes (decohere → one-way decouple → breakdown). This work is part of the YAGC (Yoshida-AI-Generated Cosmology) project, developed through collaborative dialogue between a human researcher and AI systems.