Geometric Origin of the Top Quark Yukawa Coupling from M2-Brane Dynamics in M-Theory Compactification on G₂-Holonomy Manifolds

A first-principles derivation of the top quark Yukawa coupling yₜ = 1 − αEM from M-theory compactified on a G₂-holonomy manifold (Joyce orbifold T⁷/ (Z₃ ⋉ I*), Betti numbers (b₂, b₃) = (27, 451) ). The top quark is identified with the M2-brane wrapping the minimal associative three-cycle with Euler characteristic χ = 1, yielding a bare Yukawa coupling of exactly unity. The Dirac-Born-Infeld action with Dirac-quantised electromagnetic flux introduces a self-energy correction reducing the effective tension. The worldvolume supersymmetry constraint on the superpotential, combined with canonical normalisation, yields yₜ = 1 − αEM + O (α²). The predicted top quark mass mₜ = (1 − αEM) × v/√2 = 172. 83 ± 0. 04 GeV agrees with the experimental value 172. 76 ± 0. 30 GeV at the 0. 24σ level, with theoretical uncertainty smaller than experimental precision by a factor of seven. The naive square-root scaling yₜ = √ (1 − αEM), predicting mₜ = 173. 47 GeV, is excluded at 2. 4σ, providing empirical discrimination between DBI expansion schemes. Three additional parameter-free predictions are derived from the same geometric hierarchy: the charm quark mass mc = αEM × v/√2 = 1. 270 GeV (<0. 1% error), the tau lepton mass m_τ = αEM × v = 1797 MeV (1. 1% error), and the Cabibbo mixing angle sin θc = (αEM/2√2) ^1/4 = 0. 2254 (0. 4% error). The last result constitutes an ab initio derivation of the Cabibbo angle from the fine-structure constant alone, without quark mass ratios or adjustable parameters. A Bayesian model comparison yields a Bayes factor of 10⁸ ("decisive" on the Jeffreys scale). All predictions employ the same three measured inputs (αEM, v, sin²θc) and the same G₂ geometry used in the companion Geometric Standard Model analysis of fifteen Standard Model observables (Zenodo DOI: 10. 5281/zenodo. 19256313) and in the resolution of the cosmological lithium problem (Zenodo DOI: 10. 5281/zenodo. 19266022). Paper: 9, 363 words, ~20 pages, 64 equations, 7 tables, 4 figures, 4 appendices, 161 references.