Local Constraint Restoration Stabilizes Coherent Histories Under Irreversible Record Formation

The emergence of a single, coherent classical world requires more than a macroscopic arrow of time. While irreversible record formation establishes temporal ordering, it does not by itself ensure that macroscopic histories remain mutually consistent rather than fragmenting into incompatible configurations. We study a minimal network-based model in which local records accumulate irreversibly, generating time but not necessarily global coherence. We show that, in the absence of a consistency-restoring mechanism, macroscopic states fragment even under causal dynamics. Introducing constraint restoration stabilizes coherence; critically, this restoration need not be diffusive, acausal, or globally optimized. A single, strictly local, finite-speed constraint update per timestep suffices to suppress inconsistency, even on adversarial frustrated graphs and as system size increases. These results identify local constraint restoration as a minimal structural requirement for macroscopic coherence under irreversibility, and provide a concrete instantiation of the Coherence–Selection Interface Theory framework for selection under constraint [10]. Keywords: arrow of time, irreversibility, macroscopic coherence, decoherence, consistent histories, graph Laplacian, local constraint restoration