ok curved surface energy analytic pressure matches volume finite differences: 4.89e-10 ok full dilution/capillary Hessian agrees with finite differences and symmetry ok far height and pressure are independent boundary data; bath volume never sets h ok nonflat state dilutes monolayer using curved surface area: area ratio 0.999261637 ok reverse curved geometry force matches independently evaluated energy: 1.04e-09 ok flat uniform monolayer retains zero reference energy and force ok small-slope constant-coverage limit matches inherited capillary energy: -2.82e-09 ok actual curved-area mechanics and common-state drainage converge ok nonzero motion conserves liquid including bath accounting and material S ok common free energy and inherited dissipative metric satisfy global inequality ok every shared face uses exactly one signed liquid flux 11 passed, 0 failed