Elimination of René Peschmann's 968 Remaining Hard Fibers for the Perfect Cuboid Problem

Abstract

Recently, René Peschmann proved perfect-cuboid nonexistence on 1,072 explicit master-tuple fibers with $\max (m,n)\le 100$, leaving 968 fibers in the same bounded parameter range. In this paper, I eliminate all 968 remaining fibers. Most fibers fall to fairly short rank-zero or covering arguments, while the final cases need the stronger local-global sieves. Together with Peschmann's theorem this excludes perfect cuboids on all 2,040 admissible fibers with $m\le 100$; the result is still a bounded-fiber theorem rather than a proof of the full perfect-cuboid conjecture.