ok actual coupled solver completes ledger test ok fractional ownership integrates exact clipped regional area ok liquid geometric and relative-flux ledgers close separately ok nonzero material surface transfer without centroid relabelling ok capillary pressure, area, shape, metric, ownership product rule closes ok uniform-reference monolayer area and ownership energy closes ok real coupled trajectory activates shape and geometry work ok paired regional exchange cancels ok independent native total energy agrees with regional components ok missing transport is detected rather than balanced with a residual source 10 passed, 0 failed