Finite CRT Run Geometry, Shared-Core Transfer, and Prime-Layer Modalization on the 6k ±1 Candidate Axis

This paper consolidates the finite CRT structure behind the local run geometry of the 6k±1 candidate axis. It has three aims: first, to formulate the local obstruction of a run prefix exactly; second, to decompose the covariance and cancellation structure of the finite CRT survivor field into shared cores; and third, to describe the transition produced by adjoining new prime moduli as a finite transfer operator and to diagonalize it modally.