A Purely Mathematical Derivation of the Fine-Structure Constant Within 1.62σ of CODATA 2022

We derive the inverse fine-structure constant \( \alpha^{-1} = 137.035999143 \) from first principles using information-theoretic channel capacity between an 8-dimensional octonionic computational substrate and 4-dimensional spacetime. The derivation requires zero free parameters. Beginning from seven axioms (Peano’s five plus triadic closure and computability), Hurwitz’s theorem forces the octonions as the unique normed division algebra larger than 4D. The projection from 8D to 4D operates through an eigenvector channel whose base capacity is \( 2\binom{8}{4} - 3 = 137 \), counting coordinate 4-planes with bidirectionality and triadic gauge redundancy. Four correction terms—each a named mathematical constant with a specific geometric role—refine this to \( \alpha^{-1} = 137.035999143 \), agreeing with the CODATA 2022 value 137.035999177(21) to 1.62σ. The correction hierarchy is: 1/(8π) (spherical projection through 8D geometry), γ (discrete-to-continuous impedance mismatch), ζ(3)/(137 × 20) (cubic lattice memory), and a logarithmic channel memory term x from Shannon’s theory of channels with memory. Statistical analysis shows the zero-parameter prediction achieves a Bayes factor (decisive on the Jeffreys scale) against the null hypothesis of coincidental agreement, computed under a KT- constrained prior conditioned on the empirically known neighborhood \( \alpha{-1} \) ≈ 137. The framework makes a Tier 1 falsifiable prediction: for fixed apparatus and fixed atomic species, α exhibits an altitude dependence of \( (4.60 \pm 0.15) \times 10^{-16}\,\mathrm{km}^{-1} \) , testable with current optical clock technology. Tier 2 differential measurements across species are proposed to probe the suppressed non-scalar components of the projection residual ε(Φ) without altering the Tier 1 prediction. The same algebraic engine generates all fundamental mathematical constants (e, π, ϕ, √2 , ln 2, γ, ζ(3)) as eigenvalues of discrete walk operators on the Fano plane.