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The research aims to classify Standard Model particles using a geometric structure in six dimensions.

April 21, 2026Open Access

Geometric Classification of Standard Model Particles Derived from the Orientation Structure of the 6-Dimensional Hypercube

Key Points

The research aims to classify Standard Model particles using a geometric structure in six dimensions.
Expanded the hypercube framework to include a sixth axis for color labeling.
Derived properties like color charge and quark-lepton distinction from the geometric model.
Produced 62 Standard Model states without using free parameters.
Successfully reproduced all 62 Standard Model states from the geometric structure.
Derived 8 distinct gluon states based on geometric principles.
Identified graviton placement and calculated mass as signed area.

Abstract

Extending the 5-dimensional hypercube framework by adding a sixth axis Q (discrete color label with 4 values 0, r, g, b), this paper derives color charge, quark-lepton distinction, 8 gluon states (3×3−1=8), graviton placement, and mass as signed area from a unified discrete geometric structure. All 62 Standard Model states are reproduced without free parameters.

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Noriaki Kihara

System Equipment (China)

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Geometric Classification of Standard Model Particles Derived from the Orientation Structure of the 6-Dimensional Hypercube

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