The perfect cuboid problem is equivalent to finding points on the curves w² = λ⁸ + Aλ⁴ + 1 with new elliptic obstructions excluding some families but no unconditional non-existence proof.
Asiryan, Irreducibility of the cuboid polynomialP a,u(t) via a rank-zero elliptic curve, arXiv:2510.11768 (2025)
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Quartic reductions and elliptic obstructions for perfect Euler bricks
The perfect cuboid problem is equivalent to finding points on the curves w² = λ⁸ + Aλ⁴ + 1 with new elliptic obstructions excluding some families but no unconditional non-existence proof.