This work demonstrates that the entire hierarchy of special unitary groups SU (n) is generated by a single fundamental parameter χ = 616. A unique fourth-degree polynomial is proven to exist: n (k) = (69/8) k⁴ - (777/25) k³ + (63/8) k² + (2029/50) k with rational coefficients that reproduce all key groups of the hierarchy: SU (7) → SU (0) → SU (26) → SU (2) → SU (52) → SU (507) → SU (1905) →. . . Key results: - All polynomial coefficients are exact rational fractions, indicating the discrete arithmetic nature of the hierarchy- Connections are found between coefficients and Fibonacci numbers: 63 = 3 × F₈- Approximate identities connect coefficients to χ = 616 and φ = (1+√5) /2- The canonical chain is established: χ ↔ SU (26) ↔ n (1) = 26 ↔ n (k) ↔ the entire hierarchy- χ acts as a dynamic parameter that fixes the entire infinite hierarchy of gauge groups This work is the second part of the Σ-Ω⁴ Omega Unified Physics trilogy. Contents: - dynamicₕierarchyₐrticleᵣu. pdf — Russian version- dynamicₕierarchyₐrticleₑn. pdf — English version- dynamicₕierarchyₐrticleᵣu. tex — LaTeX source (RU) - dynamicₕierarchyₐrticleₑn. tex — LaTeX source (EN) - DYNAMIC HIERARCHY GENERATION. py — Python implementation- dynamicₕierarchyᵣesults. json — Complete analysis results License: Universal Academic Licence v1. 0 (UAL-v1. 0) Commercial use prohibited without author's written permission. Related work: - SU (0) Operator: Projection onto the Energy-Vacuum Condensate DOI: 10. 5281/zenodo. 20855845
Sergey Viktorovich Matershov (Thu,) studied this question.