Discrete Hexagonal Lattice Dynamics: A Block Universe Formulation of Photon Indivisibility, Wave-Particle Duality, and Quantum Non-Cloning

Abstract Standard quantum mechanical interpretations rely on non-deterministic wave-function collapse (Copenhagen), continuous branching of physical realities (Many-Worlds), or unobservable non-local guiding fields (De Broglie–Bohm) to account for single-photon indivisibility, anti-bunching, and wave-particle duality. Here, we present a deterministic alternative formulated on a four-dimensional static block universe whose spatial spatiality is governed by a discrete hexagonal lattice. Photon paths are modeled as fixed, pre-calculated trajectories regulated by a Mod 9 numerical invariant and bounded by the 5184\text{ Hz} frequency threshold (\Omega_0 = 72^2). Phase propagation along lattice nodes is controlled by the 3I temporal gating sequence \mathbf{S}_{3I} = (8, 13, 8, 5, 13, 8) and thermal stabilization via a 7-cycle periodic break (\Lambda_7). We demonstrate that photon anti-bunching and the no-cloning theorem are structural imperatives of the discrete lattice geometry rather than statistical artifacts, offering a unified, non-probabilistic framework for quantum optic observations.