This work develops a refinement—deterministic arithmetic framework for the odd-to-odd Collatz dynamics. The admissible inverse mapR(n; k) = (2^k n - 1) / 3is governed locally by residue—phase conditions on the live classes 1 and 5 (mod 6) and refines coherently through the exponential modulus towerM_j = 2 * 3^(j+1).At each level, admissibility of finite k-words depends only on the residue modulo M_j, and refinement introduces additional phase coordinates without ambiguity.Globally, admissible inverse lifts generate disjoint affine rails whose minimal bases are uniquely determined. Independently, the dyadic valuationk = v_2(3m + 1)produces an exact slice decomposition of the odd integers with weights 2^(-k). We prove that the affine rail partition and the dyadic slice decomposition coincide exactly, yielding a single unified arithmetic structure in which every odd integer possesses a unique admissible ancestry.A refinement-induced acyclicity principle is established: no finite admissible k-word remains compatible across all refinement levels M_j. Periodic inverse instruction regimes are destroyed by phase shifts under refinement, excluding nontrivial odd cycles. Moreover, compatibility across the refinement tower forces every infinite admissible chain to realize a base residue in the anchor structure; hence no divergent trajectory can occur.Finally, the forward mapT(m) = (3m + 1) / 2^(v_2(3m + 1))is shown to be the exact algebraic inverse of all admissible inverse lifts. Forward and inverse dynamics therefore coincide on a single closed affine system anchored at 1.Consequently, the odd-to-odd Collatz dynamics admit a complete internal arithmetic classification, and every forward trajectory converges to the fixed point 1.