The Synchronization Latency Principle: Geometric Coherence, Informational Audit, and the Emergence of Inertia and Mass

We formulate an operational hypothesis—the Synchronization Latency Principle—as a disciplined extension of an “Information Audit” viewpoint within a locality-preserving quantum cellular automaton (QCA) framework. The central claim is scoped so it can be scrutinized: matter-like excitations are auditable images that are not certified at a single-site update, but only after an audit closes over a minimal local neighborhood. In three dimensions, a nearest-neighbor stencil suggests a (1+6) block of cardinality 7; under explicit circuit-locality and audit assumptions, we show a structural lower bound Daudit ≥ 7 on the micro-depth needed to incorporate all neighbor links into a joint certification. We then strengthen the theory beyond narrative plausibility by adding (i) an operational definition of copy time via Helstrom hypothesis testing, (ii) a quantum-speed-limit lower bound on τcopy via QFI/Bures geometry and a stiffness parameter χ, and—crucially for PRA standards—(iii) a minimal explicit translation-invariant QCA class (a 7-layer Floquet-QCA schedule) for which the small-momentum dispersion has an emergent effective mass meff derived from the circuit. In that class we prove a proposition: the certified-sector quasi-energy satisfies E(k) = p (veff∥¯hk∥)2 + (meffc2)2 +O(∥k∥2, θ2, ∥k∥θ), ith veff ∝ 1/Daudit and meffc2 ∝ √ χ/Daudit, both directly testable in QCA simulation. Finally, Planck→electroweak matching is kept as a discussion (not a result): it is presented only as a possible UV boundary-condition narrative, explicitly separated from the structural theorems.