A Closed-Form Formula for the Fine-Structure Constant from the QCD Parameter z = β₀ + N_c i

We report an empirical closed-form expression for the electromagnetic fine-structure constant α with no free parameters. The formula decomposes 1/α into three physically distinct contributions: modular geometry (e^π, 53%), gauge topology (Vol(SU(2)) = 2π², 45%), and a QCD Fibonacci–Padé dressing (β₀/N_c, 2%). All coefficients derive from a single complex QCD parameter z = β₀ + N_c·i = 7 + 3i. The self-consistent solution yields 1/α = 137.035 999 190 890 07..., matching CODATA 2022 at +0.66σ (10 significant digits). Statistical tests (52M random functions, blind test, PSLQ, parameter uniqueness scan) suggest the match is unlikely to be accidental. Substituting this α into the neutron mass formula from a companion paper, the ratio m_n/m_e is reproduced to 9.8 digits with zero experimental input. The 11th digit of 1/α is predicted and falsifiable by experiments ~2027–2030. This is a first preprint version; the presentation is preliminary and being refined.