Mathematical Framework for Probabilistic Localization and Multi-Parameter Reconstruction of Neutrino Interactions on Earth’s Surface Using Advanced Triangulated Detector Networks, Machine Learning Integration, and Covariance-Aware Likelihood Optimization Abstract Neutrinos, as weakly interacting leptons with flavor eigenstates admixed via the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix and exhibiting quantum mechanical oscillations modulated by mass-squared differences Δm_ij² and mixing angles θ_ij, … Continue reading Mathematical Framework for Probabilistic Localization and Multi-Parameter Reconstruction of Neutrino Interactions on Earth’s Surface Using Advanced Triangulated Detector Networks, Machine Learning Integration, and Covariance-Aware Likelihood Optimization