From UD Theory to the Fine Structure Constant: A First-Principles Derivation

This paper derives a fundamental dimensionless constant κ from first principles within the UD theory framework, and identifies it with the fine structure constant α. UD theory is a metatheoretical framework based on four fundamental axioms. From these axioms, a four-aspect structure emerges: UU (dark energy), UD (dark matter), DD (visible matter), and DU (quantum fluctuations). The equilibrium background values are UU = UD = 1/4 and DD = DU = 1/ (4e^π). Two structural constants are identified from the extreme limits: π (singularity rejection index from the black hole limit) and e^π (vacuum rejection index from the vacuum limit). The universal evolution constant κ is the critical result of the U-D competition. It is the product of six factors, each with a clear physical origin: 1. 1/2 — the starting point (critical state U = D = 1/2) 2. 1/π — singularity rejection constraint (prevents D → 1) 3. 1/e^π — vacuum rejection constraint (prevents U → 1) 4. 1/2 — the two attributes U and D (subjects of competition) 5. 3 — the three products: matter, space, and time6. 1/√2 — quantum normalization (from total normalization axiom) Combining these factors yields: κ = (1/2) · (1/π) · (1/e^π) · (1/2) ·3· (1/√2) = (1/ (2πe^π) ) · (3/ (2√2) ) = 3/ (4√2 π e^π) Numerical evaluation gives κ = 1/137. 03. The experimentally measured fine structure constant is α = 1/137. 036 (CODATA 2022). The two values agree to within 0. 03%. Therefore, we identify κ = α. The fine structure constant, historically known as the strength of electromagnetic interactions, is revealed to be the universal evolution constant—the critical result of the U-D competition that governs both the symmetry breaking from the critical state and all subsequent cosmic evolution. Electromagnetic interactions are one phenomenological manifestation of this underlying constant. No free parameters, no fitting, no external assumptions. Every factor follows necessarily from the UD axioms and established results.