Chebyshev Bias and Golden Phase Structure mod 5

We study three structures attached to the modulus 5 in analytic number theory: the Chebyshev bias E(x) = #{p ≤ x : p ≡ ±2 mod 5} − #{p ≤ x : p ≡ ±1 mod 5}; its spectral reconstruction from the non-trivial zeros of the Dirichlet L-function L(s, χ₅); and the golden phase lock of Paper 125 (DOI 10.5281/zenodo.19022277), in which the ratio of two character projections P(χ₂)/P(χ₃) at zeros of ζ(s) is phase-locked to the line at angle arctan(1/φ) in the complex plane. The phase lock, originally numerically observed at 50 zeta zeros to 40-digit precision, admits a textbook derivation from the L-function functional equation for the odd conjugate-pair characters χ₂, χ₃ mod 5. We give that derivation explicitly. The…