AI-Assisted Elliptic Curve Ranks and the Perfect Cuboid Polynomial Constraint — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The perfect cuboid problem is linked to rank-zero elliptic curves via an irreducible degree-8 "cuboid polynomial," while recent AI-assisted searches push elliptic curve ranks to ≥29–30, suggesting deep constraints on rational Diophantine structures. | MATH: Cuboid polynomial Pa,u(t) (even monic degree 8) from Sharipov's first-cuboid specialization; irreducibility proven for nonzero integers a,u with u2 ≠ a2 via a rank-zero elliptic curve model. Elliptic curve rank records: ≥29 (2024) and ≥30 (AI-discovered, Dr. Samuel Allen Alexander). Quartic models y2 = x4 + ax3 + bx2 + cx + d used for divisibility-by-2 and D(q)-quintuples (Yesin). | CONNECTION: Rank-zero elliptic curves correspond to finite rational point sets — a discrete symmetry akin to crystallographic point groups (no continuous deformation). The degree-8 polynomial's irreducibility echoes octonionic/E8 root system structure (8 dimensions, rank 8). The perfect cuboid's edge ratios, if s
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026aiassisted,
title = {{AI-Assisted Elliptic Curve Ranks and the Perfect Cuboid Polynomial Constraint — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635258},
url = {https://zenodo.org/records/23635258},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - AI-Assisted Elliptic Curve Ranks and the Perfect Cuboid Polynomial Constraint — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635258
UR - https://zenodo.org/records/23635258
AB - FINDING: The perfect cuboid problem is linked to rank-zero elliptic curves via an irreducible degree-8 "cuboid polynomial," while recent AI-assisted searches push elliptic curve ranks to ≥29–30, suggesting deep constraints on rational Diophantine structures. | MATH: Cuboid polynomial P_a,u(t) (even monic degree 8) from Sharipov's first-cuboid specialization; irreducibility proven for nonzero integers a,u with u^2 ≠ a^2 via a rank-zero elliptic curve model. Elliptic curve rank records: ≥29 (2024) and ≥30 (AI-discovered, Dr. Samuel Allen Alexander). Quartic models y^2 = x^4 + ax^3 + bx^2 + cx + d used for divisibility-by-2 and D(q)-quintuples (Yesin). | CONNECTION: Rank-zero elliptic curves correspond to finite rational point sets — a discrete symmetry akin to crystallographic point groups (no continuous deformation). The degree-8 polynomial's irreducibility echoes octonionic/E_8 root system structure (8 dimensions, rank 8). The perfect cuboid's edge ratios, if s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -