The Standard Model contains 19 free parameters whose values lack theoretical explanation. We present a geometric framework deriving these constants from topological invariants of a seven-dimensional G₂-holonomy manifold K₇. The framework contains zero continuous adjustable parameters. All predictions derive from discrete structural choices: the octonionic algebra O, its automorphism group G2 = Aut(O), and the unique compact geometry realizing this structure. 18 dimensionless quantities achieve mean deviation 0.087% from experiment, including exact matches for N_gen = 3, Q_Koide = 2/3, and m_s/m_d = 20. The 43-year Koide mystery receives a two-line derivation: Q = dim(G₂)/b₂ = 14/21 = 2/3. Exhaustive search over 19,100 alternative G₂ manifold configurations confirms that (b₂=21, b₃=77) achieves the lowest mean deviation (0.23%). The second-best configuration performs 2.2× worse. No alternative matches GIFT's precision across all observables (p 4σ after look-elsewhere correction). The prediction δ_CP = 197° will be tested by DUNE (2034–2039) to ±5° precision. A measurement outside 182°–212° would definitively refute the framework. The G₂ metric admits exact closed form φ = (65/32)^{1/14} × φ₀ with zero torsion, verified in Lean 4. Whether these agreements reflect genuine geometric structure or elaborate coincidence is a question awaiting peer-review.