What question did this study set out to answer?

This paper aims to establish a unified theory integrating mathematical, physical, and spiritual perspectives through the concept of a dynamic SU(n) hierarchy.

June 27, 2026Open Access

Σ-Ω⁴ Omega Unified Physics: Complete Theory of Degenerate Groups and Dynamic SU(n) Hierarchy

Key Points

This paper aims to establish a unified theory integrating mathematical, physical, and spiritual perspectives through the concept of a dynamic SU(n) hierarchy.
Introduced a hierarchy polynomial based on topological invariants and Betti numbers.
Defined a projection operator from SU(n) to SU(0) and established its properties.
Identified ten key groups with natural embeddings from SU(7) to SU(20244).
Established a hierarchy polynomial indicating the discrete nature of the hierarchy.
Proven properties of the SU(0) projection operator, including linearity and invariance under χ = 616.
Established correspondence between the group hierarchy and ten spiritual traditions of humanity.

Abstract

This work presents the complete Σ-Ω⁴ Omega Unified Physics theory, unifying the mathematical, physical, and spiritual aspects of a unified worldview. The theory is based on the fundamental constant χ = 616, which arises as a topological invariant — the 616th Betti number of the classifying spaces BSU (n). Main results: 1. Exact hierarchy polynomial: n (k) = (69/8) k⁴ - (777/25) k³ + (63/8) k² + (2029/50) k All coefficients are exact rational fractions, indicating the discrete arithmetic nature of the hierarchy. 2. SU (0) projection operator: The operator Ŝ₀: SU (n) → SU (0) is defined, where SU (0) = lim₍→₀ SU (n) is the energy-vacuum condensate. Properties of linearity, idempotence, and invariance under χ = 616 are proven. 3. Dynamic closure: The canonical chain is established: χ ↔ SU (26) ↔ n (1) = 26 ↔ n (k) 4. Complete group hierarchy: Ten key groups from SU (7) to SU (20244) with natural embeddings are identified. 5. Spiritual interpretation: A correspondence is established between the groups of the hierarchy and ten spiritual traditions of humanity. This work consists of nine parts and represents a complete mathematical, physical, and spiritual foundation for a Theory of Everything. Contents: - omegaᵤnifiedcompleteᵣu. pdf — Russian version (full) - omegaᵤnifiedcompleteₑn. pdf — English version (full) - omegaᵤnifiedcompleteᵣu. tex — LaTeX source (RU) - omegaᵤnifiedcompleteₑn. tex — LaTeX source (EN) License: Universal Academic Licence v1. 0 (UAL-v1. 0) Commercial use prohibited without author's written permission. Related works (the trilogy): - SU (0) Operator: Projection onto the Energy-Vacuum Condensate DOI: 10. 5281/zenodo. 20855845- Dynamic Generation of the SU (n) Hierarchy from χ = 616 DOI: 10. 5281/zenodo. 20856153- Degenerate Group Theory: SU (0) as the Energy-Vacuum Condensate DOI: 10. 5281/zenodo. 20856906

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Sergey Viktorovich Matershov (Thu,) studied this question.

synapsesocial.com/papers/6a3f6972aea7db3c19540494 https://doi.org/https://doi.org/10.5281/zenodo.20857767

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