← The Perfect Cuboid: from the Continuous World and Radix Representation to Arithmetic Freedom
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Center-Axis Rational Closure Theorem (v0.1)
The Perfect Cuboid: from the Continuous World and Radix Representation to Arithmetic Freedom
Center-Axis Rational Closure Theorem (v0.1)
unsigned in the source
The Perfect Cuboid Center-Axis Rational Closure Theorem: An Exact Reformulation of the Perfect Cuboid Problem as Rational Closure on a Low-Dimensional Coupling Surface
A perfect cuboid exists iff there are rationals t_a, t_b, t_c ∈ (0, 1) with Σ((1 − t²)/(1 + t²))² = 1 (t_a = f/(g + a) etc.), with an explicit integer-witness generator; the seed (448, 495, 840; 1073) lies on this surface at t = (25/39, 17/28, √(233/1913)).
An exact but elementary equivalence (the Pythagorean-triple parametrisation); §52 of the paper: 'so the classical Perfect Cuboid is still not solved by this paper'.
The labels 'Theorem 1', 'Canonical Research Anchor' and 'complete proof' over-dignify an elementary equivalence. The seed is a near-miss in which six of the seven lengths are integers: only the face diagonal √445729 = √(233·1913) is not; it is not a perfect cuboid.
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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.