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 y_t = 1 − α_EM 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 y_t = 1 − α_EM + O(α²). The predicted top quark mass m_t = (1 − α_EM) × 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 y_t = √(1 − α_EM), predicting m_t = 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 m_c = α_EM × v/√2 = 1.270 GeV (<0.1% error), the tau lepton mass m_τ = α_EM × v = 1797 MeV (1.1% error), and the Cabibbo mixing angle sin θ_c = (α_EM/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 (α_EM, v, sin²θ_c) 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.