What question did this study set out to answer?

The aim is to explore the combinatorial properties of a 6-dimensional hypercube with a new label axis.

April 26, 2026Open Access

Set-Theoretic Structure and Combinatorial Properties of the 6-Dimensional Hypercube — Spin Classification, Set Enumeration, and Sign Product

Key Points

The aim is to explore the combinatorial properties of a 6-dimensional hypercube with a new label axis.
Defined a 6-dimensional hypercube structure by appending a 4-valued axis Q to a 5-dimensional hypercube.
Examined the set-theoretic structure through combinatorial enumeration.
Transformed the Q-axis from a 3-bit to a 2-bit representation.
Reduced total states from 21 to 13 through the new structure.
Identified three color states for quarks in the new classification.
Demonstrated anti-quarks maintain the same color with spatial sign flip.

Abstract

v7: Q-axis restructured from 3-bit (8-valued) to 2-bit (4-valued: Q=2c₂+c₃). Q=0 orthogonal to Q-axis (colorless/lepton), Q∈1, 2, 3 = 3 colors (quark). Anti-quarks carry same color (spatial sign flip only). Total states reduced from 21 to 13. This paper defines a 6-dimensional structure obtained by appending a 4-valued discrete label axis Q to a 5-dimensional hypercube, and derives the combinatorial properties of its set-theoretic structure through pure combinatorial enumeration without physical terminology.

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Discussion

Authors

Noriaki Kihara

Actions

Institutions

System Equipment (China)

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Set-Theoretic Structure and Combinatorial Properties of the 6-Dimensional Hypercube — Spin Classification, Set Enumeration, and Sign Product

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Cite this study