Stability of an astigmatic correction choice: a finite-menu analysis

Preprint — not peer reviewed. This mathematical report examines whether a preferred astigmatic correction remains preferred throughout a stated uncertainty set. It applies established nearest-point and support-function geometry to a fixed, finite correction menu, and separates predicted residual cylinder, stability of the choice, and the largest excess squared residual from retaining it. An exact rational-arithmetic implementation check covered 1,600 constructed cases and 1,995 nominal-choice comparisons, with agreement between formula-based and direct squared-loss calculations. The package provides the manuscript, mathematical derivation, local protocol, verification source and recorded output. These are constructed mathematical cases, not patients. The uncertainty sets are not independently calibrated, and the work does not estimate postoperative accuracy, visual benefit or spectacle independence. Squared-loss regret has units D²; its square root is not additional residual cylinder. The manuscript describes AI assistance with research, preparation and editing, mathematical derivation and Python code.