The Origin of α = 1/137: Derivation from CAS Cost Structure to Metric Signature (5,2) and the Wyler Volume Ratio

The low-energy fine-structure constant α ≈ 1/137.036 remains unexplained. Wyler (1969) 2reproduced it via the volume ratio of D5 = SO(5, 2)/[SO(5) × SO(2)] but could not ad- 3dress the Robertson–Gilmore criticisms (absent physical motivation, arbitrary group se- 4lection, non-unique measure). We introduce 4 axioms + 1 lemma modeling physical 5change as Compare-And-Swap (CAS) operations, and prove (Theorem 1) that the irre- 6versible/reversible cost classification is structurally equivalent to a quadratic form’s pos- 7itive/negative signs. This forces the metric signature (5, 2); via SO(5, 2) → D5, four of 8five Wyler factors are self-derived (the (·)1/4 exponent is borrowed from Wyler’s origi- 9nal). Result: 1/α = 137.036 082 (relative deviation 6 × 10−7, zero fitting parameters). The 10framework also yields sin2 θW = 7/(2 + 9π) = 0.23122 (matching MS at MZ) in five for- 11ward steps, forced by the framework’s two-reading principle (cost vs norm) plus standard 12arithmetic. The internal DOF 7 = 4 + 3 matches the Steane code [[7, 1, 3]] decomposition. 13Finally, using only α and sin2 θW , we derive the baryon-to-photon ratio ηB = 6.14 × 10−10, 14within 0.4σ of Planck’s (6.12 ± 0.04) × 10−10 as an RLU coupled access working hypothesis, 15falsifiable by future CMB precision. This record contains both the English version (alpha137_en.pdf, primary) and the original Korean version (alpha137_kr.pdf).