This paper completes a six-part program reducing the Riemann Hypothesis, within the Hilbert–Mellin framework, to a single representation-theoretic obstruction. The final analytic barrier—Linear Collision Sparsity (M0)—is shown to be equivalent to the absence of almost-invariant vectors for a unipotent shear acting on the prime-support subspace of an adelic quotient. The argument is driven by a scaling obstruction: near-invariance under the shear at resolution T−1T^{-1}T−1 would require persistence of spectral mass at the dilation fixed point despite exponential conjugation by the diagonal flow. Using non-commutation and dilation theory, polynomial decay of low-frequency shear mass is enforced for vectors with finite diagonal Sobolev regularity. Since the prime vector admits only polylogarithmic diagonal growth, spectral concentration is impossible. The result replaces probabilistic heuristics with a structural incompatibility enforced by adelic geometry. The reduction is unconditional, modular, and representation-theoretic in nature.