We study Wilson lattice Yang—Mills theory on ℤ³ in a gauge that fixes one link at every site along a period-3 forest, in which every free link shares a plaquette with exactly seven other free links. Two results follow.

(A) For SU(2), a single-link Dobrushin argument with the sharp one-quarter Kantorovich estimate of Bhattacharjee and Bhattacharya gives a unique infinite-volume state, invariance, reflection positivity, exponential decay of correlations and a transfer-matrix gap m ≥ −log(7β_W/4) for β_W < 4/7. The same estimate gives β_W < 1/3 in three dimensions without gauge fixing and β_W < 1/2 in the temporal gauge. As Bhattacharjee, Bhattacharya and Lockwood showed for 1/3 in four dimensions, we show that 4/7 is the ceiling of this argument for every gauge-fixing forest.

(B) For every compact group with a faithful unitary representation, the Hessian of Σ_p Re Tr Q_p restricted to the free links is bounded in absolute value by h = 9.599991, uniformly in the field. The proof is a site-plus-plaquette certificate with rational data: its finite part is checked in exact rational arithmetic, and positivity of a two-parameter family of matrices of size at most 12 is proved with outward-rounded interval arithmetic. With the Bakry—Émery criterion this gives log-Sobolev inequalities, a unique state and an explicit gap for N|β| < κ_G/h; for SU(N) this is |β| < 1/(2h) ≈ 1/19.20, compared with 1/32 of Shen, Zhu and Zhu and 1/24 from the sharp un-gauge-fixed constant. An exact computation at the trivial field shows that no bound below 9.3479 is possible in this gauge. All statements are at strong coupling and fixed lattice spacing.