Derivation of the Universal Evolution Constant in UD Theory and Its Identification with the Fine Structure Constant

We derive the universal evolution constant E of UD theory from first principles. The derivation traces the complete, logically inevitable cosmic evolutionary chain: symmetry breaking from the critical state U = D = 1/2, the vacuum rejection constraint e^π (inherited from the black hole standing-wave condition via exact U ↔ D duality), the singularity rejection constraint π, the input-output ratio 3/2 (proved by exhaustive classification of the irreducible products of two attributes under mutual containment, with the global U = D condition identified as the necessary prerequisite for the sustained competition that constitutes time), and the orthogonal-basis projection factor 1/√2. The resulting expression E = 1/2 · 1/e^π · 1/π · 3/2 · 1/√2 contains no adjustable parameters and yields E⁻¹ ≈ 137.101. The physical chain connecting E to the electromagnetic coupling is established: E governs the fundamental UD competition strength; the electromagnetic interaction, mediated by the DU channel, inherits this strength at the quantum-projected level. Based on numerical consistency with the CODATA 2022 fine structure constant α⁻¹exp = 137.035999084 (deviation 0.047%, attributable to QED radiative corrections) and this physical chain, E is identified as α. In UD theory, this single constant manifests in three distinct roles—symmetry-breaking threshold, local condensation threshold, and electromagnetic coupling—each reflecting the same underlying UD competition strength in a different physical context.