← Method Lines of the Perfect Cuboid: FORC, GERES, SIO-X4, X4-DMSD, IGPC and TIFV
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FORC-P7 and P8 · a bounded face-height certificate
Method Lines of the Perfect Cuboid: FORC, GERES, SIO-X4, X4-DMSD, IGPC and TIFV
FORC-P7 and P8 · a bounded face-height certificate
unsigned in the source
Frontier-Only Height-Bounded Enumeration and the Coverage Bridge, and the Incremental Height Ladder: No Perfect Cuboid When the Three Primitive Face-Triple Hypotenuses Are ≤ 20000
P7: there is no perfect cuboid whose three primitive face-triple hypotenuses are all ≤ 5000: 792 primitive fractions, 204 ordered exact face triples, 34 Euler-brick worlds, every one with a non-square space diagonal (a non-residue mod 7/17/19/23). P8: extends the same certificate incrementally to H_E ≤ 10000 (1593 fractions, 60 worlds) and ≤ 20000 (3186 fractions, 624 ordered triples, 104 worlds), all rejected by the body-modular gate, with from-scratch equivalence hashes and idempotent SQLite re-entry.
A bounded certificate: no perfect cuboid in this small range, not nonexistence.
The wording 'completeness / nonexistence certificate' and 'Bounded Proof Package' holds only in this explicitly stated small range; the coverage bridge of P6 is accounting and is not needed for validity. All counts and witness distributions were reproduced by independent brute force in the pre-publication read-through. This height H_E (hypotenuses of face triples) is a different quantity from g (the space diagonal) of Phase 1D in the core, and the numbers cannot be compared.
Connections · Connections
This is a full-text translation of the Chinese source, which remains authoritative for its research claims. Translation is not independent mathematical verification and does not upgrade the original evidence level.