Shadowed Faces and Residue-Affine Dynamics in Cone-Monotone Integer Relations

This paper develops the exact arithmetic structure generated by shadowed bad faces in cone-monotone homogeneous integer equality relations. It identifies the first persistent boundary mechanism lying beyond finite Kleene convergence and shows that, in physical dimension two, this mechanism is governed by one-dimensional guarded residue-affine dynamics with a common expanding rational multiplier.…