Supplement Number

Supplementary Material for "The inverse capillary-rise problem: conditioning, resolution limits, and the comparability of contact angles". Contains the numerical methods and their verification (S1-S4), the eleven-point historical benchmark recovered from primary sources (S5), derivations of the meniscus expansions and the radial surface-tension gradient (S2, S6), framework-dependence and re-inference tables (S7), the consistency-diagnostic positive control and admissibility map (S8), design tables and the discriminating power of the validating experiment (S9-S10), and the analyses added in revision: the spherical-cap bias of the force-balance inversion and the conditioning of the sessile-drop route (S11).