Symmetry & Logic deprivation of the fine structure constant

Abstract We give a theorem–proof derivation of a dimensionless constant coin- ciding with α−1 to twelve decimal places, using only exact rational arith- metic. The central object is the twisted anisotropic Epstein sum C(τ,η) = m∈Z3 \{0} 1−cos(2πm1 η) 3/2 , η= 148. m2 1 +τ2 m2 2 +τ4 m2 3 We prove absolute convergence, analytic duality C(τ,η) = τ−3C(τ−1,η), unique- ness of the stationary point τ⋆ > 0, and an exact rational enclosure of C(τ⋆,η) by a finite block plus a closed analytic tail bound. A fixed rational map Φ ∈ Q(x), monotone on the established interval, yields the final rational enclosure for the output constant. A machine-checkable certificate (exact fractions and two SHA–256 hashes) is specified for byte-identical reproduction. No floating-point arithmetic appears anywhere.