What question did this study set out to answer?

The paper aims to define and explore the properties of a 6-dimensional hypercube by adding a discrete label axis.

April 26, 2026Open Access

Set-Theoretic Structure and Combinatorial Properties of the 6-Dimensional Hypercube (v9)

Puntos clave

The paper aims to define and explore the properties of a 6-dimensional hypercube by adding a discrete label axis.
Introduces an 8-valued discrete label axis Q to a 5-dimensional hypercube.
Derives classifications and products through combinatorial arguments.
Presents an example mapping the derived states to Standard Model particles.
Enumerates 62 derived states from the hypercube structure.
Establishes new spin classifications for these states.
Introduces an open problem regarding the state count on the Q-axis.

Resumen

Defines a 6-dimensional structure by adding an 8-valued discrete label axis Q to a 5-dimensional hypercube. Derives spin classification, set enumeration, and sign products from purely combinatorial arguments. Section 9 presents an interpretation example mapping the 62 derived states to Standard Model particles plus the graviton. Version 9: Added open problem note on Q-axis state count.

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