A delta-recurrence for Winkler's Corollary 9 and a robust implementation for n >= 9

This technical note states a general recurrence for the Step 2 transition in Mike Winkler's parity-vector generation (Corollary 9) for the 3x+1 stopping-time structure. The formula holds for all n in N and all j >= 1 and is derived directly from the Diophantine term formula (Theorem 3). It closes the case explicitly left open in Corollary 9 for n >= 9 with j >= 2.
We provide a compact reference implementation in Python that solves the Diophantine equation exactly and uses the delta-recurrence as a fast path, and we validate the result numerically for n=9..12: 130/130, 182/182, 730/730, and 2741/2741 Step-2 neighbor pairs (j >= 2) pass the stated congruences and the Mod-8 class (delta == 1 mod 8 for odd n, delta == 3 mod 8 for even n).
The note is part of an AI publication experiment; readers should treat it as AI-assisted work and consult the project record for scope and limitations.
For background, see M. Winkler, "The Recursive Stopping Time Structure of the 3x+1 Function" (arXiv:1709.03385, v4, 2024).
For context on the experiment, see the retrospective (DOI 10.5281/zenodo.17232247).