The ray-class repair for affine systems: the class group as the index of definable scalings

For a non-principal prime p of a number field the affine Bost-Connes-type monoid is not well defined over the ring of integers. This paper proves that the obstruction is itself the invariant: with h the order of [p] in the class group, the globally definable scalings form exactly the subsemigroup hN of the local valuation semigroup, so the minimal repaired system is the h-step system scaled by a generator pi of p^h. The exterior-tower Pimsner-Voiculescu computation of the companion paper applies verbatim with q^h in place of q = N(p): the class of the unit has exact order N(p)^h - 1, so the order of p in the class group survives in K_0 as the exact torsion order of [1], and the intermediate layers contribute Z/|q^h +- 1 - Tr(pi)| for quadratic fields, computed explicitly in Q(sqrt(-5)) at the non-principal prime above 3 (K_0 contains Z + Z/8 with [1] of order 8, K_1 contains Z + Z/2). The class group enters as torsion, not rank. Remaining problems are recorded: separating q from h beyond the composite q^h (the dual coaction is the candidate), the Galois descent from the Hilbert class field where capitulation principalizes p and Gal = Cl_K acts, and the several-prime case where definable scalings are the kernel of Z^S -> Cl_K.