Positive-Energy Warp Solitons: An Energy-Condition Audit of the Lentz Construction

In 2021 Lentz proposed warp configurations sourced by positive-energy structures, challenging the assumption that every warp bubble needs negative Eulerian energy density. This audit evaluates the claim's arithmetic at its published scale: a one-hundred-metre structure carrying one hundred Jupiter masses of source has a mean density of 4.53e+22 kilograms per cubic metre, utterly negligible against the ceiling of 9.72e+57 kilograms per cubic metre, and the Eulerian density in the core is positive as claimed. However, positivity for one family of observers is not the null energy condition: in the schematic wall model evaluated here, 0.31 of sampled radial null directions at the wall still violate the null energy condition. The verdict is measured: the construction is a genuine advance that retires one slogan, that warp needs negative density everywhere, and it does not retire the energy-condition problem, which reappears in the null form at the wall. Computed schematically, not measured.