Validation of Fundamental Subatomic Constants via a Discrete Four-Dimensional Body-Centered Cubic Lattice Framework

This paper presents a formal derivation and validation of the fine-structure constant (alpha), the muon to electron mass ratio (m_mu / m_e), and the muon decay constant (tau_mu) within the framework of the Coherent Field Model (CFM). Using a discrete four-dimensional Body-Centered Cubic (BCC) lattice to represent the vacuum manifold, we show that these fundamental constants emerge naturally from lattice stability, torsional harmonics, and coordinated behavior of neighboring lattice nodes, rather than existing as free parameters. Key contributions include: A quantitative mapping of subatomic mass ratios to torsional harmonics in a BCC lattice. A structural derivation of the fine-structure constant based on phase-evaluation cardinality and lattice neighborhood multiplicity. A stochastic model of muon decay incorporating the coordinated recovery of local BCC neighborhoods, providing insight into emergent lifetime properties. Numerical results showing high agreement with experimental benchmarks: m_mu / m_e (99.99 percent), alpha (99.5 percent), and tau_mu (84 percent). This work offers a mechanical and geometric basis for electromagnetic coupling and particle mass ratios, potentially providing new avenues for exploring the vacuum structure and subatomic dynamics.