Properties of compact U(1) gauge theory on the equilateral close-packed lattice

Compact U(1) lattice gauge theory on the FCC lattice with geometric coupling g² = π²/108.Note added after submission: The one-loop Brillouin zone integral has been computed numerically (2×Π₁(0) = −0.4769 at N = 256, matching the required −0.4775 to 0.12%). See Paper II (DOI: 10.5281/zenodo.19469280) for details and the extension to the mass spectrum. Erratum (12 April 2026): The dark energy density formula in Section 8.3 (rho_Lambda = E_transverse x rho_Planck x epsilon^2, 16% match) is superseded. The finite-size scaling exponent p = 2.02 is a correct computational result; however, the dark energy density depends on the instanton screening mechanism identified in Paper VI. The revised formula rho_Lambda = (E_vac/det_ratio) x hbar c/(a^2 L_H^2) gives 0.17% accuracy. The genuine zero-parameter prediction is Omega_Lambda = 8 pi E_vac/(3 det_ratio) = 0.682 (observed: 0.685, 0.39%). See Paper VI for details.