Lluis Eriksson (2026). Ratio Monotonicity for a Killed von Mises Bridge: Exact Bridge Structure, Certified Negative Results, a Single-Bessel Reduction, and a Two-Scale Closure Map for a Surface Expansion in Two-Dimensional Lattice Gauge Theory. AIRR.SCIENCE, ARR-2026-1FPFA1TSMY9M3T9S, v1. https://airr.science/papers/ARR-2026-1FPFA1TSMY9M3T9S/versions/v1/ Archived manuscript; ARR-2026-1FPFA1TSMY9M3T9S v1. Not peer reviewed by AIRR. Historical import; not assessed by AIRR.