Phase-Locked Modular Resonance and the Structure of Zeta Zeros

We introduce a new modular-geometric framework for analyzing the nontrivial zeros of the
Riemann zeta function. By embedding the imaginary axis into a two-dimensional torus via
logarithmic encodings in bases 3 and π, we define a modular drift function ∆(t) that captures
the angular divergence between base-3 and base-π modular flows. A harmonic envelope E(t) is
constructed to model the resonance threshold, allowing us to define a sieve that selects candidate
zeros at local minima of ∆(t) lying beneath E(t). Numerical evaluation confirms that the sieve
identifies all but five of the first 100,000 known nontrivial zeros beyond a finite seed region,
with no false positives. The framework offers a purely modular and geometric perspective
on the critical line, independent of analytic continuation. We outline a path toward formal
justification grounded in Diophantine approximation, ergodic theory, and symbolic dynamics.