ok reverse geometry gradient matches finite differences of inherited surface/capillary/disjoining/gravity energy: 4.53e-10 ok moving area Jacobian matches independent finite differences and global fixed-domain closure ok reservoir-aware differentiated and inherited energy use the same excluded capillary faces ok uniform monolayer/thickness has no spurious force on irregular support ok incremental inertial/viscous objective and actual-geometry gradient agree ok centered exact-gradient Hessian-vector agrees with objective gradient difference ok actual energy-driven particle motion converges: displacement 1.600e-05, Newton 3 ok material inventories unchanged and measured moving energy/kinetic/viscous budget closes ok anchored frame positions and velocities stay fixed ok actual relative drainage and shared donor momentum transfer preserve uniform translation ok passive momentum mixing does not inject kinetic energy and accounts for pinned-support impulse ok pinned-support external impulse exactly accounts for open free-particle momentum ok unsupported soluble closure is rejected instead of silently dropping chemical energy ok actual moving/open-drainage liquid, surface amount and independent reservoir-work energy budget close ok fourfold bath bookkeeping capacity does not change film motion or one-sided hydraulic mobility: 2.22e-16 ok stable uniform-reference surface energy preserves the original physical force ok repeated infeasible trial stays rejected instead of reading a stale cached energy ok constitutive counterexample retained: normal-only Cartesian faces miss shear, full gradient recovers analytic shear dissipation ok full-gradient body viscosity is rigid-rotation/translation invariant away from imposed walls ok full symmetric-gradient and divergence form reproduces analytic affine dilation ok Dirichlet velocity samples act at real outer faces instead of clamping a mesh-width fluid band ok shared face-pyramid correction dissipates alternating cell velocities rather than a centered-gradient null mode 22 passed, 0 failed