A Unified Cosmological Model on Emergent Discrete Time via Traversal of Fixed 4D Voxel Matrix: Resolving Temporal Genesis, Kinematic Decoupling of Local Dynamics, and Apparent Cosmic Acceleration

This paper presents a comprehensive cosmological framework designed to reconcile the smooth continuum of General Relativity with Planck-scale quantum discreteness. We model the fundamental background geometry of the universe as an immutable, pre-existing 4D matrix of spatial voxels. First, we resolve the problem of temporal genesis: spatial and temporal pixels existed prior to the Big Bang in a globally dormant, frozen state (\Delta t_{\text{global}} = 0), and the Big Bang corresponds to the initial activation event (\kappa = 0 \to 1) triggered by the propagation of a Cosmic Frontier, sequentially generating temporal quanta (Chronons). Second, we prove the Decoupling Theorem: global discrete temporal progression, generated by boundary activation, is mathematically orthogonal and kinematically decoupled from localized physical state transitions governed by cell-bounded Hamiltonians ([\hat{\mathcal{A}}, \hat{H}_{\mathbf{n}}] = 0). Third, we provide a complete geometric alternative to Dark Energy: under a constant linear boundary propagation (v_{\mathcal{F}} = \text{const}), the spherical geometry of the lattice causes the number of active photon-traversed voxels between observers to accumulate non-linearly over time. To a relativistic observer analyzing redshift, this optical-geometric interaction mimics an accelerating expansion (\ddot{a} > 0), fully accounting for Type Ia supernovae observations without invoking exotic repulsive energy densities. By synthesizing Digital Physics, Causal Dynamical Triangulations (CDT), and Relational Timeless Physics, this framework offers a unified, testable account of temporal inception, local physical transitions, and cosmological acceleration.