← The Perfect Cuboid: from the Continuous World and Radix Representation to Arithmetic Freedom
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Global Closure 01 · Reframing
The Perfect Cuboid: from the Continuous World and Radix Representation to Arithmetic Freedom
Global Closure 01 · Reframing
unsigned in the source
Reframing the Perfect Cuboid: It Is Not Primarily an Integer Search Problem
By homogeneity an integer perfect cuboid exists iff the four quadratic relations have a nondegenerate positive rational solution, so the problem is recast as rational (not integer-height) existence, stated only as Hypothesis PC-RC.
A preparatory research draft (Phase 0); the paper: 'this paper does not claim that a perfect cuboid must exist, nor infer existence of rational points from the infinitude of the real solution space'.
This is the first of eight (item 01/08); paper 08 ('Upper and lower bounds of the solution space and a second expansion') is announced in every header and table of contents but is not in the package. 'Closure' in the series means closing the conceptual framework (Phase 0 — Conceptual Closure), not a result.
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.