Complete Determination of the 26 Standard Model Parameters from Three Geometric Constants in M-Theory Compactification on G₂-Holonomy Manifolds

All 26 free parameters of the Standard Model have been expressed as functions of three geometric constants K₀ = 90. 005, CLIG = 0. 05954, and CQG = 0. 665 arising from the compactification of M-theory on the Joyce orbifold T⁷/ (Z₃ x I*) with G₂ holonomy and Betti numbers (b₂, b₃) = (27, 451), supplemented by the electromagnetic fine-structure constant alphaEM and the Higgs vacuum expectation value v as experimental inputs. The derivation has employed four structural elements of the compact manifold: the Z₃ orbifold symmetry (three fermion generations and the Georgi-Jarlskog factor), the Z₅ subgroup of the binary icosahedral group I* (four CP phases from C₃ flux quantisation), the golden ratio phi = (1+sqrt (5) ) /2 inherited from the icosahedral geometry (weak mixing angle), and M2-brane instantons on associative three-cycles (cosmological constant). The predicted parameters have included: six quark masses (mean deviation 2. 5%), three charged lepton masses (mₘu/mₜau = CLIG at 0. 13%), three neutrino masses (m₂ = 8. 87 meV at 1. 2 sigma), four CKM elements (|Vᵤb| = Vcb sqrt (alphaEM) at 3. 1%), six PMNS parameters (sin² theta₁3 at 1. 7%), the strong coupling constant (alphaₛ = 0. 1170 at 0. 7% from anomaly-mediated supersymmetry breaking at m₃/₂ = MPl e^-K₀/pi = 879 TeV), the weak mixing angle (sin² thetaW = 3/ (8 phi) at 0. 23%), the Higgs boson mass (mH = 123--126 GeV bracketing the experimental value 125. 25 GeV), and the cosmological constant (rhoLambda = b₃ sqrt (2) MPl⁴ e^-pi K₀ at 1. 4%). The mean deviation across 22 observables with experimental counterparts has been 2. 8%, with a median of 1. 5%. No prediction has exceeded 2 sigma. The complete set of 26 predictions has exhibited no conjectural assignments: eight parameters have been rigorously derived and eighteen partially derived with identified assumptions. The discrete structure of the orbifold group A₅ = I*/Z₂ has been fully utilised: Z₂ for CP protection, Z₃ for three generations and the Georgi-Jarlskog factor, and Z₅ for all four CP phases (deltaCKM = 72 degrees, deltaPMNS = 216 degrees, alpha₂1/2 = 144 degrees, alpha₃1/2 = 288 degrees). This completeness has left no residual discrete freedom in the framework. Testable predictions have included: wino dark matter at 2. 4 TeV (accessible to HL-LHC), neutrino mass sum 61. 3 meV (testable by DESI), PMNS CP phase 216 degrees (testable by DUNE and Hyper-Kamiokande), and Majorana phases (testable in neutrinoless double beta decay). This is paper number 12 in the Quantum Geometric Unification (QGU) programme, unifying and extending results from 11 companion publications covering quark masses, lepton masses, neutrino mixing, gauge coupling unification, cosmology, strong CP problem, black hole information paradox, neutron star properties, and Big Bang nucleosynthesis.