Hyperbolic Bias and the Geometric Exclusion of Riemann Zeta Zeros

This paper presents a theoretical framework aimed at examining the Riemann Hypothesis (RH) through the lens of a differential interaction operator Φ(s,δ) acting on the Hilbert space l2(N). By mapping the Dirichlet η-function to a trace-class operator, we analyze the resulting phase torque J(δ,t), which is governed by a hyperbolic sine bias. We propose a product criterion wherein the operator trace vanishes if and only if a zero exists at mirrored coordinates across the critical line. Furthermore, we explore how the Diophantine independence of prime logarithms, when amplified by the hyperbolic lever, may mathematically restrict the trace from vanishing off the critical line Re(s) = 1/2. Within the constraints of this oper ator construct, the analysis suggests a geometric mechanism consistent with the confinement of non-trivial zeros to the critical line.