The Perfect Cuboid: from the Continuous World and Radix Representation to Arithmetic Freedom
G2E.3 and G2E.4 · Mordell–Weil sieves
unsigned in the source
The 2-Primary Mordell–Weil Compatibility Sieve and the Dual-Quotient Mordell–Weil Sieve: Sylow-2 Projection, Clean-Prime Boundary Forcing and an Exact Genus-3 Height Exclusion
Using primes where #E_0′(F_p) is a power of 2, every rational point of C_2 must lie in one torsion coset and in 24 explicit 2-adic residue disks mod 2^18 (two of which are the known degenerate boundary lifts); at p = 11, 59, 181, 197, 1669, compatibility with both rank-one quotients forces h to a boundary residue, so any non-boundary rational point of C_2 has 38,622,984,917 | uv(u² − v²); an exact scan of C_2 (denominator ≤ 20000, 121,590,395 states) finds no non-boundary point.
An exact partial sieve plus a bounded exact exclusion; the papers: 'the fixed slice k = 7/32 has not yet been globally eliminated' and 'the output is not yet a complete classification of C_2(Q)'.
The scan source g2e3_power2_scan.cpp of G2E.3 is a stub ('See g2e3_metrics.json'), so the sieve cannot be regenerated from the package alone (the prime list and the boundary lifts do re-check). The pre-publication read-through reproduced the group-size table and re-ran the genus-3 scan for v ≤ 1200: no hits.