The Perfect Cuboid: from the Continuous World and Radix Representation to Arithmetic Freedom
Phase 1F-D · Restriction on the space diagonal
unsigned in the source
Phase 1F-D: The Global Diagonal Restriction Re-derived in the Fixed-g Framework
The space diagonal of a primitive cuboid is neither a prime power p^e (for any e, by a Chebyshev-polynomial rational-root argument) nor a product of two distinct primes (two elementary Diophantine branches), so the first surviving type is g = p²q.
A classification of a sub-family: the status line reads 're-derived independently; known in the literature (Korec, 1992)'.
This is a re-derivation of a known result, not a new one; the attribution to Korec 1992 was not checked. Both arguments were re-derived by hand and by computer (rational roots for e ≤ 10) in the pre-publication read-through. Phases 1F-A, 1F-B, 1G and 1H are earlier or redundant write-ups of the same result; see the download table below.