A Kinematic-Geometric Criterion for the Zeros of the Riemann Zeta Function Based on a Symmetric and Asymmetric Reformulation

This paper develops a kinematic-geometric framework for the Riemann zeta functionbased on the center-of-mass dynamics of finite Dirichlet sums. Interpreting the partial sums as a weighted Dirichlet walk, we study the accumulation of its normalized centerof mass and identify an asymptotic helical structure arising fromEuler--Maclaurin summation. Within this framework, zeta zeros are characterized by the disappearance ofleading residual wobble in the center-of-mass evolution. Analyzing the induced wobble dynamics, we decompose the forcing into symmetricand asymmetric components and show that the asymmetric contribution vanishes onlyon the critical line Re(s)=1/2. This yields a geometric rigidity mechanism linking the absence of residual wobbleto critical-line localization of nontrivial zeros.