Vacuum Mechanics: One-Loop Mass Formula, the Koide Derivation of α⁻¹ = 137, and Complete Standard Model Accounting

We correct, extend, and complete the Vacuum Mechanics framework developed in Papers I–VIII. Four errors are corrected (KK mass, BH horizon, flatness, muon g-2). Seven of eight open problems are resolved, including the origin of α⁻¹ = 137. All six next-to-leading-order mass correction coefficients are derived from the one-loop QCD beta function with N_f = 6 active flavors (b_QCD = 7), with zero free parameters. All nine fermion masses are predicted at 0.14% RMS. The Koide relation Q_K = 2/3 uniquely selects N = 137 as the fine-structure constant inverse. Of 26 Standard Model parameters, 19 are derived at sub-0.5% accuracy with zero fitting from a single input (v = 246.22 GeV). Seven failures and one open problem (the acoustic experiment) are documented.