One sterile neutrino model to explain four separate anomalies

A single 3+1 neutrino framework, where a sterile state experiences a novel matter potential tied to ordinary or dark matter density, mimics standard three-flavor non-standard interactions at low energies while revealing a distinct four-flavor resonance near 10 TeV. The model resolves the NOvA–T2K tension, accounts for the anomalous electron-neutrino excess in Super-Kamiokande atmospheric data, and aligns with the IceCube spectral hint — all with a very small muon-sterile mixing that avoids conflict with muon-neutrino disappearance bounds. The parameter space is directly testable: KATRIN is sensitive to the required electron-sterile admixture at the predicted mass-squared splitting of ~60 eV².