A Conditional Strong-Coupling Gap Estimate for a Periodic Two-Row SU(2) Gauge Ladder

This research note presents a conditional proof candidate for a volume-uniform lower bound on the excitation gap of a fixed-spacing, one-dimensional, periodic two-row SU(2) lattice gauge ladder. It derives an explicit candidate strong-coupling threshold and coefficient from stated activity, polymer-counting, Kotecký–Preiss, tail, and short-period estimates. The claim remains conditional: the polymer bound and count, endpoint argument, operator-domain assumptions, gauge-sector transfer, and matching to the cited perturbation theorem have not received independent mathematical certification; comparison with prior work is incomplete. This is not a certified theorem, not a four-dimensional continuum Yang–Mills result, not a numerical diagonalization at enormous volume, and not a solution of the Yang–Mills existence and mass-gap problem. The note is offered for scrutiny and correction. A locally run language model assisted with exploratory arithmetic and organization; its output was not treated as proof or independent evidence. No external mathematical review has certified this note.