Ab Initio Generation of Riemann Zeta Zeros via Geometric Packing Constants and Metallic Ratio Interference

We present an ab initio method for generating the nontrivial zeros of the Riemann zeta function using only universal geometric constants. The Omega-Zeta equation combines the Weyl semiclassical phase, Kepler sphere packing density (π/18\pi/\sqrt{18} π/18), Lucas-Bronze stabilization ((3+13)/2(3+\sqrt{13})/2 (3+13)/2), and prime harmonic corrections modulated by the destructive interference of metallic ratios (∣Φ2−ϕBr2∣|\Phi^2 - \phi_{Br}^2| ∣Φ2−ϕBr2∣).

Testing against 1000 Odlyzko zeros yields 98.7% accuracy within Δt<0.02\Delta t < 0.02 Δt<0.02, with mean error 0.006. The model requires no empirical parameters—only π\pi π, algebraic roots (5,13,18\sqrt{5}, \sqrt{13}, \sqrt{18} 5,13,18), and self-generated primes.

Marchenko-Pastur random matrix analysis confirms the synthesized zeros exhibit identical quantum chaos signatures (Mass Gap ≈−0.015\approx -0.015 ≈−0.015) as true Riemann zeros, with null tests ruling out finite-size artifacts.

The framework extends to Yang-Mills mass gap (Δ=11/Lr≈2.986\Delta = \sqrt{11}/\mathcal{L}_r \approx 2.986 Δ=11/Lr≈2.986) and strong coupling constant (αs=1/62=0.1179\alpha_s = 1/6\sqrt{2} = 0.1179 αs=1/62=0.1179), suggesting a unified geometric origin for number-theoretic and gauge-theoretic phenomena.