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The fine-structure constant α ≈ 1/137 appears throughout quantum electrodynamics with no theoretical explanation for its value in the Stan- dard Model. We present a complete derivation of α from the axiomatic foundations of the Kosmoplex framework—a deterministic, 8-dimensional computational theory. Our derivation yields α−1 = 137.035577, agreeing with the measured value 137.035999177(21) , relative error (3.1 × 10−6, or 0.0003%), without empirical input. We provide rigorous proofs for each component: (1) the combinatorial base 137 from octonionic structure, (2) the rotational correction 1/8π from phase space requirements, and (3) the projection distortion γ/137 from discrete-to-continuous mapping. We predict gravitational variation ∆α/α = (1.23±0.15)×10−15 per kilometer altitude, testable with current atomic interferometry. This demonstrates that fundamental constants emerge from mathematical necessity rather than arbitrary parameters.