We propose S₀, a geometric model in which the critical line Re(s) = 1/2 is interpreted as the axis of a spiral phase resonator parameterized by three constants π, e, and φ. An anchored calibration variant, fixing the first zero t₁ = 14.134725 as the phase origin, reduces the mean absolute error from 1.29 (Backlund) to 0.436 (S₀) for n = 2–50 — a 3× improvement. The anchored variant uses t₁ as a single external input; all remaining parameters are derived analytically from π, e, φ without fitting. Both models achieve comparable spacing rhythm correlation r(Δt) ≈ 0.69; the S₀ advantage lies in positional accuracy, not spacing rhythm. A diagnostic analysis of residuals over n = 1–2000 reveals operator-dependent asymmetry: S₀ residuals show A = 0.44 (p < 10⁴) versus A = 0.05 (p⁻ = 0.68) for Backlund, with no invariant subspace across operator classes. S₀ is not a proof of the Riemann Hypothesis but a verifiable geometric approximation with explicit predictions. This study did not receive a specific grant from any funding institution in the public, commercial, or non-profit sectors.
Yurii Serednytskyi (Mon,) studied this question.