The Ford-Damped Operator Family: The Boundary Re s = 1/2, a Totient Moment, and an Eisenstein-Coefficient Comparison

We prove three anchor theorems and report one measured phenomenon; everything else is an explicitly open program, and no part of RH is claimed. Theorem A (existence dichotomy and zeta norm) [proved]. Theorem B (Hurwitz diagonal) [proved]. Theorem C (rescaled boundary limit) [proved]. The Dirichlet-series identity is classical; the contribution claimed here is only the stated operator-family route to the finite sums and their ordered limit. It belongs to the arithmetic operator and Branch C research program. This is a corrected preprint edition released under the Creative Commons Attribution 4.0 license.