Emergence of Observable Excitations and Temporal Ordering from Holonomy-Constrained Lattice Dynamics

We propose a discrete pre-geometric framework in which observable structure, entropy growth, and the cosmological arrow of time emerge from local violations of holonomy-induced null states on an infinite-dimensional lattice. inspired by holonomy structures appearing in Loop Quantum Gravity, we interpret the multiplicative identity of oppositely oriented holonomies as a fundamental local null condition. Configurations satisfying this condition are defined as v-entities and represent perfectly balanced vacuum-like states of the lattice. We show that local neighbour interactions can destabilize these balanced configurations, producing localized excitations that violate the null condition. These excitations, termed nullity-broken entities (NB-entities), constitute the first nontrivial observable structures of the theory. Their formation induces irreversible configurational rearrangements across neighbouring lattice regions, thereby increasing block entropy under coarse graining. Within this framework, time is not introduced as a fundamental background parameter. Instead, temporal ordering emerges dynamically from the monotonic growth of configurational entropy generated by NB-entity formation and interaction. The model therefore provides a microscopic mechanism linking holonomy structure, symmetry breaking, entropy production, and the emergence of the cosmological arrow of time within a fully discrete lattice framework.