Adelic Shear Dynamics and the Reduction of the Riemann Hypothesis to Quantitative Mixing

In a preceding sequence of papers, the Riemann Hypothesis was reduced within the Hilbert–Mellin framework to a single quantitative obstruction: Linear Collision Sparsity (Hypothesis M0), a near-diagonal bilinear constraint on prime-power coefficients. Papers 4–5 established that all far-field and oscillatory contributions are unconditionally controlled by discrete Calderón–Zygmund geometry, leaving M0 as the unique remaining analytic obstruction. In this paper, we give a complete operator-theoretic characterization of M0 via adelic dynamics. We construct an explicit unipotent one-parameter flow on the adelic quotient space of $\mathrm{GL}_2$ and show that quantitative decay of matrix coefficients for this flow implies M0. As a result, the Riemann Hypothesis is reduced to a concrete representation-theoretic hypothesis: polynomial mixing of the adelic shear on the spectral support generated by prime powers. The reduction is unconditional, structurally precise, and employs only standard tools from automorphic representation theory and ergodic theory. No Fourier-analytic energy estimates, no spectral heuristics, and no universality assumptions are used. The remaining obstruction is isolated as a single, falsifiable mixing property of a specific adelic operator.