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

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_{n→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:- omega_unified_complete_ru.pdf — Russian version (full)- omega_unified_complete_en.pdf — English version (full)- omega_unified_complete_ru.tex — LaTeX source (RU)- omega_unified_complete_en.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