Pocket Geometry and the Warp Energy Bill: Van den Broeck Reduction Arithmetic

Van den Broeck's modification keeps a warp bubble's internal radius at one hundred metres while shrinking the radius the outside universe sees, and with it the radius that enters the energy integral. Because the integral scales as the external radius squared, a neck of one centimetre cuts the requirement from 1.01e+47 joules to 1.01e+39 joules, and a ten-micrometre neck cuts it to 1.01e+33 joules, a mass equivalent of 1.12e+16 kilograms, with a reduction factor of 1.0e-14. This is the one published reshaping that truly changes the arithmetic, and this paper states its achievement at full size. The verdict nonetheless remains negative: the residual bill is still negative energy in quantities no source supplies, and the neck's own geometry concentrates the gradients the integral was spared from counting. Computed, not measured.