Neutrino Masses and Dark Matter in the Noncommutative Geometric Unification Framework

his work completes the Standard Model particle spectrum within the noncommutative geometric unification paradigm by resolving neutrino mass generation and dark matter stability. Key innovations include: (1) Seesaw mechanism via θµν-condensate with MR ∝ ⟨θ2⟩/MPlanck, (2) Sterile dark matter tensors nµν stabilized by topological invariants HTr(n ∧ n) = 2πk, and (3) Entropic protection of mass hierarchies mνi ∝ exp(−i 2/2αν). The model predicts PMNS mixing angles θij ∝ exp(−|i^2 − j^2|/2βν), direct detection cross sections σSI ∝ (⟨θ⟩/Λ)4, andtestable signatures for neutrino-less double beta decay (|mee| ≈ 0.03 eV) and darkmatter annihilation lines (Eγ = mDM).