The Geometry of the Critical Line: A Monograph on the SCT 5-Manifold, the Prime Translation Group, and the Riemann Zeros.

This monograph presents a geometric characterization framework for the Riemann critical line $\sigma=1/2$, comprising an eight-paper series and an addendum. It constructs a 5-dimensional Riemannian manifold ($M^5_{SCT}$) compatible with the functional equation of the Riemann zeta function. Within this metric space, the critical line is shown to be geometrically distinguished in five complementary senses: it is the unique totally geodesic slice, derivative-decoupled, parity-compatible with the functional equation isometry, DADA-coherent under Hurwitz continued fraction projection, and amplitude-symmetric. Furthermore, the primes are geometrically realized as a dense translation group acting on the transverse…