Degenerate Group Theory: SU(0) as the Energy-Vacuum Condensate

This work develops a theory of degenerate groups in which SU(0) is defined as the limit SU(0) = lim_{n→0} SU(n) and interpreted as the energy-vacuum condensate — the quantum vacuum, śūnyatā. The group hierarchy:SU(7) → SU(0) → SU(26) → SU(2) → SU(52) → SU(507) → SU(1905) → ... is generated by the exact polynomial n(k) with rational coefficients. Key results:- SU(0) is defined as the energy-vacuum condensate — the quantum vacuum, śūnyatā- Complete hierarchy of groups SU(n(k)) for k = -1, 0, 1, ..., 8 is established- Group embeddings are investigated and subgroup indices are computed- A correspondence is established between the groups of the hierarchy and ten spiritual traditions of humanity: - SU(7) — Zoroastrianism (fire and light) - SU(0) — Buddhism (śūnyatā, emptiness) - SU(26) — Judaism (law and structure) - SU(2) — Christianity (love and interaction) - SU(52) — Islam (fullness and completion) - SU(507) — Hinduism (multiplicity and unity) - SU(1905) — Taoism (the way and nature) - SU(4992) — Shinto (spirits and nature) - SU(10718) — Jainism (non-violence and asceticism) - SU(20244) — Sikhism (devotion and service) - Predictions are made for new groups for k = 9, 10, 11, 12, 13 This work is the third part of the Σ-Ω⁴ Omega Unified Physics trilogy. Contents:- degenerate_group_theory_article_ru.pdf — Russian version- degenerate_group_theory_article_en.pdf — English version- degenerate_group_theory_article_ru.tex — LaTeX source (RU)- degenerate_group_theory_article_en.tex — LaTeX source (EN)- DEGENERATE GROUP THEORY.py — Python implementation- degenerate_group_theory.json — Complete analysis results License: Universal Academic Licence v1.0 (UAL-v1.0)Commercial use prohibited without author's written permission. Related works:- 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