Hyperbolic Bias and the Geometric Exclusion of Riemann Zeta Zeros

We present a formal analytical framework for the Riemann zeta function by mapping the Dirichlet η(s) function to a trace-class interaction operator Φ(s) on the Hilbert space l2(N). By applying a normalization kernel K(s), we establish a bijective mapping between the operator trace and the Riemann zeta function throughout the critical strip. We derive the Phase-Torque J(δ,t) representing the imaginary component of the interaction trace, and demonstrate that it vanishes identically on the critical line Re(s) = 1/2 due to unitary phase symmetry. Conversely, for Re(s) ≠ 1/2, a hyperbolic bias arises from the broken symmetry of the interaction magnitudes, which, when coupled with the Diophantine independence of prime logarithms, prevents the trace from vanishing. This geometric exclusion principle rigorously confines all non-trivial zeros to the critical line, providing a proof of the Riemann Hypothesis.