Parameter-Free Prediction of the Neutrino Mass Spectrum from M2-Brane Instantons on Associative Three-Cycles of the Joyce G₂-Holonomy Orbifold

The complete neutrino mass spectrum has been derived from first principles within the Quantum Geometric Unification (QGU) framework, an M-theory compactification on the Joyce orbifold T⁷/(Z₃ ⋉ I*) with G₂ holonomy and Betti numbers (b₂, b₃) = (27, 451). Right-handed neutrino Majorana masses have been generated by M2-brane instantons wrapping associative three-cycles at the three conical singularities. The intermediate Majorana scale MR,2 = √α_EM × M_comp = 1.71 × 10¹⁵ GeV has been fixed by the supergravity hierarchy relation, while the instanton action gap δS = ln 3 + (1/7) ln K₀ = 1.742 has been determined by spontaneous Z₃ breaking in the moduli-stabilised vacuum. With democratic Dirac Yukawa couplings, the type-I seesaw mechanism has yielded m₁ = 1.56 meV, m₂ = 8.87 meV, and m₃ = 50.6 meV in normal ordering, reproducing Δm²₂₁ to 1.3% and Δm²₃₂ to 1.2%. The PMNS mixing angles sin²θ₁₂ = 0.303 (0.3σ) and sin²θ₂₃ = 0.542 (0.2σ) have emerged from tribimaximal mixing corrected by mass ratios and charged lepton contributions proportional to m_μ/m_τ ≈ C_LIG. The sum Σm_ν = 61.0 meV has been predicted, testable by DESI and CMB-S4. The mass ratios have employed zero adjustable parameters; the absolute scale has depended on M_comp = (2 ± 0.4) × 10¹⁶ GeV. The coupling C_LIG = 0.05954 has been the same constant employed in eight companion publications across particle physics, cosmology, nuclear astrophysics, and foundational physics