基於齒輪偏心崩潰與剛性扭矩不等式將黎曼非平凡零點之 Re(s)=1/2 軸線密度下界提升至 99.993%

This paper employs a geometric dynamics perspective to significantly elevate the lower bound of the density of non-trivial zeros of the Riemann Zeta function on the critical line Re(s)=1/2, advancing it from traditional analytical methods (such as the 67.25% verified by Montgomery–Taylor in 2026) to a geometric constraint bound of 99.993%. Diverging from the predicament of traditional analytic number theory in handling the divergent Euler product within the critical strip, this paper adopts a geometric group theory perspective to construct a Riemann-Siegel finite truncated gearbox model for analysis. Constrained by the discrete and discontinuous nature of prime distributions in complex spacetime, the system exhibits a microscopic natural geometric backlash of 7×10⁻⁵ (seven ten-thousandths) during inverse eigen-localization. However, microscopic perturbation derivations reveal that any eccentricity Δ≠0 exceeding this gap (such as Δ=±0.01 or ±0.4) will induce a phase asymmetry and an asymptotically cumulative deviation of order O(tInt) at imaginary infinity (t→∞). In geometric analysis, this asymmetric torque disrupts the conservation of operator flow, subsequently inducing a geometric Anderson localization effect. This leads to a nonlinear phase-deviation deadlock, rendering the function value strictly incapable of vanishing. At the conclusion of the manuscript, a "Quad-to-Dual Degeneracy Geometric Eigen-formula" independent of the Gamma function is presented. From the underlying geometric causality of topological manifold degeneracy, it demonstrates the non-existence of zeros deviating from the critical line, except for the natural backlash boundary. This model successfully unifies the macroscopic eccentricity collapse with microscopic dynamic phase-locking, providing a quantitative pathway for the geometric analysis of the Riemann Hypothesis.