Geometric Mass Generation and Topological Interaction Diagrams in the Standard Model from M-Theory Vacuum Dynamics on G₂ Manifolds

A complete derivation of fifteen Standard Model parameters from M-theory compactified on the G₂-holonomy manifold T⁷/ (ℤ₃ ⋉ I*) with Betti numbers (b₂, b₃) = (27, 451), selected as the unique physical vacuum with probability exceeding 1 − 10⁻²⁰. The fine-structure constant α⁻¹ = 137. 039 (0. 002%) has been derived from the gauge kinetic function, the hierarchy CLIG/CQG = √α from zero-mode localisation at ADE singularities, and six quark Yukawa couplings including the Cabibbo angle sin θc = (α/ (2√2) ) ^1/4 = 0. 2254 (0. 4%). Three lepton masses, top quark mass (0. 23σ), Higgs mass (0. 16σ), and muon g−2 (0. 39σ) obtained with zero adjustable parameters. Bayes factor B ≈ 10³⁹. Version 2 (April 7, 2026): Three key derivations added. (1) The factor 1/√2 in the electron mass formula derived from SUGRA constraint CLIG + CQG = 1/√2, ℤ₃ orbifold topology forcing an intermediate scattering vertex for w = 2 windings, and coherent re-emission amplitude at the vertex (Eq. 38-39). (2) Rule 1 (stable/unstable vertex assignment) derived from Born-Oppenheimer modulus dynamics: stationary states (dρ/dt = 0) yield CLIGᵗree, decaying states drive KK excitations yielding CLIGᵖhys. (3) Two α⁻¹ formulas connected via algebraic identity (Eq. 7). Limitations updated: items (iv) - (vii) reflect derived status. Eight appendices (A-H). 31 pages, 6 figures, 201 references.