DCT-SM-01 · DCT cluster

Standard-model gauge structure from McKay 2I → E₈

in Dimensional Coherence Theory

Nolan G. Parrott ORCID 0009-0009-8794-2589 Reserved DOI: 10.5281/zenodo.20032825 arXiv (primary): hep-ph

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In one sentence: The Standard Model gauge group SU(3)×SU(2)×U(1) and the three-generation fermion content derived from the McKay 2I → E₈ correspondence.

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Abstract

The Standard Model gauge group SU(3)×SU(2)×U(1) and its three-generation fermion content are derived from the McKay correspondence between the binary icosahedral group 2I — the symmetry of the 600-cell — and the affine Lie algebra \(E_{8}\). Through the standard branching \(E_{8}\)→ \(E_{6}\)×SU(3) family→SO(10)→SU(5)→SU(3)C×SU(2)L×U(1)Y, three fermion generations are forced by the (27,3) representation of \(E_{6}\)×SU(3), and the mathbbZ_3 coset partition 120 = \(3 \times 4\)0 of the 600-cell vertex set produces CKM mixing in the Yukawa sector. The proton-to-electron mass ratio is derived as \(m_p/m_e\) = z· 153 + 1/varphi^{4} + 1/\(z^{2}\) = 1836.152842, matching CODATA 1836.152734 to \(9.2 \times 1\)0^{-8}. The CP-violating phase is \(\delta\) CP = \(\pi\)/3 = 60^circ from the spinorial half-angle lift of \(C_{3}\)subsetSO(3)LsubsetSO(4)subset \(H_{4}\) to Spin(4), with residual 5.5^circ (3.6\(\sigma\)) bracketed by Standard Model running at 7^circ–12^circ. The post-hoc closures \(\sin\theta_{13}\) = (1 - 1/varphi^{4})/240 (1.69%) and \(1/\alpha\) = varphi^{5}· 4\(\pi\)·(1 - \(\mu\)^{2}/2) (0.16%) are explicitly labelled as algebraic ansatzes, not first-principles derivations, and are the targets of Programs A and B in the corpus master roadmap~. The mathbbZ_3 cosmic-string tension G\(\mu = 2.7 \times 1\)0^{-6} vs.\ Planck bound \(1.1 \times 1\)0^{-7} is documented as the structural open question of the Standard-Model sector. The paper presents the SM-from-topology content of the corpus master record~ as a standalone particle-physics test paper.

Keywords

McKay correspondencebinary icosahedral groupE_8SU(3) x SU(2) x U(1)proton-electron mass ratioCKM mixingCP-violating phaseDimensional Coherence Theory

Cite

APA

Parrott, N. G. (2026). Standard-model gauge structure from McKay 2I → E₈. Zenodo. https://doi.org/10.5281/zenodo.20032825

BibTeX 
@misc{parrott_dct_sm_01_2026, author = {Parrott, Nolan G.}, title = {Standard-model gauge structure from McKay 2I → E₈}, year = {2026}, publisher = {Zenodo}, doi = {10.5281/zenodo.20032825}, url = {https://doi.org/10.5281/zenodo.20032825}, note = {DCT-SM-01, DCT paper cluster}
}
RIS 
TY - GEN
AU - Parrott, Nolan G.
PY - 2026
TI - Standard-model gauge structure from McKay 2I → E₈
PB - Zenodo
DO - 10.5281/zenodo.20032825
UR - https://doi.org/10.5281/zenodo.20032825
ER -

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