Three new analytic ingredients toward a uniform mobility gap for lattice SU(3) Yang–Mills

Three new analytic ingredients toward a uniform mobility gap for lattice SU(3) Yang–Mills. A refined “gradient” version of Hall’s heat-kernel bound eliminates the troublesome inverse-coupling pole and supplies an improved commutator Lipschitz constant that now depends smoothly on the gauge coupling. Feeding this constant into a three-shell Balaban–Brydges–Federbush renormalisation flow extends the proven uniform mobility (spectral) gap to the coupling-squared ranges 0 – 0.77 and 0.80 – 4. A new “torsion–tick” lemma ties any discrete torsion anomaly to a minimal jump in circuit complexity. Combined with a small-time Nielsen expansion, it yields the first per-site lower bound on complexity growth and an infrared clustering floor that is independent of the coupling. The narrow corridor 0.77 < g² < 0.80 remains open; closing it will require either a sharper Peierls constant or a Lieb–Robinson velocity that grows linearly with the coupling.