Explicit strong-coupling mass gap and a robust landing interface for four-dimensional SU(2) lattice Yang–Mills theory

This record contains a preprint, three companion working notes and the verification scripts behind every computer-assisted step, for four-dimensional SU(2) lattice Yang–Mills theory with the Wilson action (β = 4/g²) at strong coupling. Main results Mass gap for β ≤ 0.419: the infinite-volume Gibbs measure is unique, gauge-invariant correlations decay exponentially, and the Osterwalder–Schrader transfer matrix has a spectral gap. There are certified lower bounds on the gap, for example 3.453 at β = 0.1 and 0.682 at β = 0.4. The method integrates out one quarter of the links exactly in a line gauge, then applies W₁ Dobrushin contraction in the chordal metric on SU(2). Robust landing interface: the same conclusions hold for perturbed actions S_W + R, where R is a local gauge-invariant perturbation. For example, they hold for β ≤ 0.405 (g² ≥ 9.88) at tolerances (δ₁, ε) = (0.01, 0.01). This is an explicit target that a renormalization-group flow from weak coupling would have to reach. Optimality: in every continuous bi-invariant metric on SU(2), the single-link Dobrushin coefficient is at least (β/4)(1 − β²/6). The chordal metric attains β/4. Companion results (Parts I–II): a line-gauge mass gap for β < 0.2887, geodesic decimation up to β ≤ 0.393, and Wilson’s area law on tori for β < 2/3. Verification. All computer-assisted steps use exact rational interval arithmetic and can be reproduced with the included Python scripts. These run 1144, 387 and 168 falsifiable checks, all of which pass, plus negative controls. Supplementary material. Working notes outline a conditional analytic-norm framework for the weak-coupling side. The preprint does not use them. Scope. All results concern the lattice theory at fixed lattice spacing in the strong-coupling region. Nothing is claimed about the continuum limit or the Clay Millennium Prize problem. The preprint includes a dated note on OpenAI’s announcement of 26 October 2026; nothing here depends on it. AI assistance. The work was carried out with computational assistance from AI systems: (Claude, Anthropic); OpenAI GPT 6 and 5.6. Responsibility for the content rests with the author.