A Lightning-Fast Three-Flavor Neutrino Oscillation Calculator in Constant-Density Matter with Built-In Uncertainty Propagation

Neutrino oscillation experiments are entering a regime where computational speed and rigorous uncertainty quantifi- cation must go hand in hand. This paper presents a compact, three-flavor oscillation calculator for constant-density matter, built around analytic expressions from Minakata and Parke [ 14 ] cross-validated against the perturbative series of Akhmedov et al. [ 13]. The implementation reaches percent-level accuracy for both appearance and disappearance channels across 0.3–5 GeV at a 295 km baseline. Two computation paths are provided: exact Hamiltonian diagonalization as a reference, and a compact perturbative approximation that is approximately 27× faster on a vectorized 500-point energy grid. Uncertainty propagation runs through either Monte Carlo sampling of the NuFIT 6.0 parameter covariance matrix [ 12 ] or a Jacobian linearization that produces confidence bands at negligible additional cost. Validation covers unitarity preservation to better than 10−10, MSW resonance reproduction, and direct benchmarking against exact diagonalization. The result is a self-contained tool suited to parameter scans, pedagogical demonstrations, and preliminary sensitivity studies in precision neutrino physics.