Maxwell Permittivity Constant Derivation out of First Principles & Lattice Values Within HoloGenesis

We show that the vacuum permittivity, ε₀, emerges naturally from a single structural assumption of HoloGenesis: one quantum per cubic-wavelength cell at the ground frequency f_cloud ≈ 160 GHz. Single-mode quantum energy: U = h·f Classical field energy in the cell: U = (1/2) · ε₀ · E_max² · V Solving for ε₀: ε₀ = 2 · h·f / (E_max² · V) Numerical evaluation: Using lattice extremal amplitude E_max ≈ 0.06 V/m: ε₀ ≈ 8.85 × 10⁻¹² F/m, matching the measured CODATA value. Consistency check: Inserting CODATA ε₀ predicts E_max ≈ 0.06 V/m, confirming internal consistency. Conclusion: ε₀ is not arbitrary; it is the measurable compliance of the lattice at its foundational frequency. © 2025 Grégoire Mommaerts, HoloGenesis. This work is protected under international copyright law.