An Experimental Determinant Model for Zeta Zeros

We present an experimental determinant model, inspired by self-adjoint scattering on a simple quantum network, whose line–phase reproduces much of the oscillatory part of the zero counting function for the Riemann zeta function. With modest tuning, the model attains RMS ≈ 0.055 on the first 600,000 zeta zeros (best small-slice sweep ≈ 0.047) and RMS ≈ 0.0197 on the first 129 zeros of a real Dirichlet L-function (mod 5). We do not claim a proof-level operator; rather, we document the architecture, its diagnostics, and transferable numerical performance as evidence that this mechanism is worth further analytic development toward the Riemann Hypothesis (RH). Background on ζ and its zeros may be found in [1, 2]; numerical context on zero statistics is provided by [3].