The Dodecahedral Vacuum Algebra: Complete Derivation of Fundamental Constants via Limit-Free Calculus Wexp/T

This paper presents the complete mathematical foundation of Structured Vacuum Theory (TVS) using the limit-free algebraic calculus Wexp/T. We derive all fundamental physical constants from the discrete geometry of a 23-channel dodecahedral lattice (V23 algebra) without recourse to real analysis, limits, or topological completeness. Key results: (1) Exact derivation of the fine-structure constant α⁻¹ = 137 + 19/23² + 1/23³ + 0.5/23³ (precision 10⁻⁹ matching CODATA); (2) Particle masses from algebraic eigenvalues: m_e = f₁₁₁ = 0.35682 (TVS units), m_μ/m_e = 23 × 3²/1² = 207, m_p/m_e = 6π⁵_TVS; (3) Complete V23 Lie algebra with 1540 structure constants f_abc from triple scalar products; (4) Emergence of Standard Model groups: SU(3)_C from 12-1-3=8 gluon modes, SU(2)_L×U(1)_Y from 3 orthogonal axes; (5) Higgs mechanism as geometric center fixation. The theory requires zero adjustable parameters, uses only 23 and φ (golden ratio), and is formulated entirely within the differential ring Wexp/T where differentiation and integration are algebraic operations without limits.