A certified uniform drift for the SU(2) Migdal-Kadanoff recursion: an invariant cone, entry into the Dobrushin region, and the U(1) contrast

Concerns the four-dimensional SU(2) Migdal-Kadanoff (MK) recursion (hierarchical lattice gauge model), not the Wilson lattice measure. That the four-dimensional MK flow reaches strong coupling was proven by Ito (1985), with a weak-coupling analysis by Mueller-Schiemann (1987); their 1985 SU(N)/U(N) bound covers dimensions below 4. This preprint adds an explicit, uniform, computer-assisted version for SU(2), block factor 2: a cone D_t of plaquette weights (nonincreasing in the rotation angle, W/K_t nondecreasing, K_t the heat kernel) is mapped by one MK step into D_t' with 1/t - 1/t' >= 0.0244 uniformly, until the iterate lies in a cone where Dobrushin's total-variation uniqueness condition holds (18 (max W - min W)/(max W + min W) <= 0.99811). For the Wilson weight at every beta_W in (0, 3.67] this gives entry after at most 71 steps. Every link is proven on paper or certified with interval arithmetic (python-flint/Arb, mpmath). The drift comes from the curvature factor theta/sin theta of SU(2); for U(1) the one-step drift on Villain kernels is exponentially small, so no uniform per-step bound holds there. Not a statement about the lattice or continuum Yang-Mills measure. Includes certificate code and logs. Caveat: the full texts of Ito, PRL 55 (1985) 558, and Mueller-Schiemann, LMP 15 (1988) 289, were not obtained, so their methods were not checked against this work.