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We investigate the muon neutrino event rate in km$^3$ neutrino telescopes dueto a number of galactic supernova remnants expected on the basis of theseobjects' known $\gamma$-ray signals. We evaluate the potential of theseneutrino signals to exhibit evidence of the sub-dominant neutrino oscillationsexpected in various neutrino mixing schemes including pseudo-Dirac scenariosand the Exact Parity Model. With ten years' data, neutrino signals from Sgr AEast should either discover or exclude neutrino oscillations governed by a$\delta m^2$ parameter in the range $10^{-12}$ to $10^{-15}$ eV$^2$. Such acapability is not available to terrestrial or solar system neutrinoexperiments.Comment: 38 pages, 4 figures, uses AAS LATEX macros v4.

Searching for Long‐Wavelength Neutrino Oscillations in the Distorted Neutrino Spectrum of Galactic Supernova Remnants