The Fine Structure Constant from Algebraic Invariants of x² − x ± 1

We show that every parameter in Wyler’s 1969 formula for the fine structure constant α is an algebraic invariant of the polynomial family x² − x ± 1, derived from three physical axioms in prior work (DOI: 10.5281/zenodo.18614906, 10.5281/zenodo.18634037, 10.5281/zenodo.18653020). The hyperbolic discriminant Δ_h = 5 determines the conformal group SO(5,2). The elliptic discriminant |Δ_e| = 3 provides the vertex prefactor. The splitting field degree [K:ℚ] = 4 fixes the spacetime dimension. The resulting expression yields 1/α = 137.04, matching experiment to four significant figures (0.003% discrepancy). No free parameters are introduced beyond the three axioms.