Demonstration of Noether Closure from a Standing Lattice in HoloGenesis

This article presents a comprehensive numerical verification that fundamental conservation laws—energy, momentum, angular momentum, and coherence quanta—emerge naturally from a standing subitron lattice. Using lattice parameters at the foundational frequency f₀ = 160.2 GHz, we compute per-tally energy densities, ρ_{f,α}, and fluxes, S_{f,α}, confirming that the four-tally continuity equation ∂t Σα ρ_{f,α} + ∇ · Σα S_{f,α} = 0 holds numerically. Beyond energy conservation, we show that symmetry in the lattice is frequency-dependent: inputs received from f_void cascade through the Slot Ladder, divide, recombine, and distribute across particle, glider, and thermal modes according to the Law of Frequency Conservation, while Divalence ensures harmonic opposition in all paired or split modes. We further demonstrate that space and time are emergent expressions of lattice frequency, with spatial geometry encoded by the arrangement of coherent modes and temporal progression defined by frequency redistribution. Orthogonal channels arise intrinsically from lattice structure to maximize coherence, allowing Noether-like currents to manifest without directional constraints on propagating excitations. Together, these results reveal that Noether symmetry is not a postulated law in pre-existing space-time, but a quantitative consequence of coherent frequency structuring. The lattice enforces universal, scale-independent symmetry, uniting energy, frequency, orthogonality, and temporal order under a single emergent principle, positioning coherent frequency as the fundamental substrate of reality. © 2025 Grégoire Mommaerts, HoloGenesis. This work is protected under international copyright law.