Kerr-Planck Cosmology in Loop Quantum Gravity: A Unified Geometric Origin for Fermion Masses and Generations

We present a unified framework in which the masses of all charged fermions in the Standard Model, the CKM mixing angles, the neutrino mass scale, the leptogenesis scale, and the dark energy density arise from the geometry of a near-extremal Kerr black hole core quantized in Loop Quantum Gravity (LQG). The gravitational sector yields the charged lepton masses with high precision, requiring no free parameters; the transverse modes of the SU(2) Ashtekar-Barbero connection on the isolated horizon determine the quark mass patterns and the CKM matrix. The Euclidean action is discretized by the LQG area spectrum, leading to a discrete family of instantons labeled by the integer number of punctures N. Physical consistency (area quantization, angular momentum quantization, entropy maximization) fixes N ≈ 106 and ˜a ≈ 0.9 without any adjustment to particle data. With these values, the model predicts mν ∼ 0.02 eV, MN ∼ 1.6 × 104 GeV, and ρΛ ∼ 10−123M4 P, all in agreement with observations. The unconditional nucleation probability peaks near N ≈ 100; anthropic selection (the requirement of viable fermion masses for structure formation) picks precisely the range N ∼ 100 that satisfies the quantum consistency conditions, making N = 106 the relevant value for observers like us. The model is falsifiable, contains no fine-tuning, and suggests a pre-Big Bang scenario in which the observable universe emerges from a quantum-gravitational core.