Total lepton number and energy balance for the deleptonization problem. The top panel plots the change in the fluid lepton number (solid black), change in neutrino lepton number (blue), cumulative neutrino lepton number that flows off the computational grid through the outer boundary (red), and the change in the total lepton number (including off-grid contributions; dotted black). Similarly, the bottom panel plots the change in the fluid energy (solid black), change in neutrino energy (blue), cumulative neutrino energy through the outer boundary (red), and the change in the total energy (including off-grid contributions; dotted black), as a function of time.