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The research aims to define the Distinction Observable Theory (DOT) through mathematical and geometric frameworks.

March 24, 2026Open Access

Distinction Observable Theory (DOT): Foundations and the Octahedral Machine (Part I)

Key Points

The research aims to define the Distinction Observable Theory (DOT) through mathematical and geometric frameworks.
Introduced the complete tripartite graph K(2,2,2) as a fundamental mathematical structure.
Examined the nilpotent boundary operator linked to the octahedron.
Analyzed geometric and topological constraints to derive logical distinctions.
Validated the significance of the tripartite graph in forming conceptual frameworks.
Demonstrated how geometric properties lead to logical and physical distinctions.

Abstract

This is Part I of the Distinction Observable Theory (DOT). It establishes the fundamental mathematical carrier of the theory — the complete tripartite graph K(2,2,2) (the octahedron) and its nilpotent boundary operator, demonstrating how geometric and topological constraints naturally give rise to logical and physical distinctions.

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Igor M. Zhuk (Sun,) studied this question.

synapsesocial.com/papers/69c2295caeb5a845df0d3bc8 — DOI: https://doi.org/10.5281/zenodo.19161120

Distinction Observable Theory (DOT): Foundations and the Octahedral Machine (Part I)

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