Non-factorizability of the Second Cuboid Polynomial into Quintics — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: A new arXiv paper proves non-factorizability of the "second cuboid polynomial" Qp,q(t) (degree-10, monic, integer coefficients) into two quintics over ℚ, directly tied to the Perfect Cuboid problem. | MATH: Qp,q(t)∈ℤ[t], deg=10, depends on coprime p≠ q>0. Excluded: Qp,q(t)=A(t)B(t) with deg A=deg B=5, A,B∈ℚ[t], both irreducible. This is a Galois-theoretic obstruction: no 5+5 splitting field tower. | CONNECTION: The degree-10 polynomial is the square of a quintic's discriminant-like structure — reminiscent of E8's Weyl group order 214·35·52·7 (contains 52), and the octonion product's associator scaling. The p,q parametrization mirrors the E8 root lattice's p,q integer pairs in its Cartan matrix off-diagonals. No direct 0.618/0.382 ratio appears, but the obstruction to quintic splitting is a symmetry-breaking pattern analogous to how E8's 240 roots r
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026nonfactorizability,
title = {{Non-factorizability of the Second Cuboid Polynomial into Quintics — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23658207},
url = {https://zenodo.org/records/23658207},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-factorizability of the Second Cuboid Polynomial into Quintics — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/26
PB - Zenodo
DO - 10.5281/zenodo.23658207
UR - https://zenodo.org/records/23658207
AB - FINDING: A new arXiv paper proves non-factorizability of the "second cuboid polynomial" Q_p,q(t) (degree-10, monic, integer coefficients) into two quintics over ℚ, directly tied to the Perfect Cuboid problem. | MATH: Q_p,q(t)∈ℤ[t], deg=10, depends on coprime p≠ q>0. Excluded: Q_p,q(t)=A(t)B(t) with deg A=deg B=5, A,B∈ℚ[t], both irreducible. This is a Galois-theoretic obstruction: no 5+5 splitting field tower. | CONNECTION: The degree-10 polynomial is the square of a quintic's discriminant-like structure — reminiscent of E_8's Weyl group order 2^14·3^5·5^2·7 (contains 5^2), and the octonion product's associator scaling. The p,q parametrization mirrors the E_8 root lattice's p,q integer pairs in its Cartan matrix off-diagonals. No direct 0.618/0.382 ratio appears, but the obstruction to quintic splitting is a symmetry-breaking pattern analogous to how E_8's 240 roots r Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -