The atmospheric neutrino mass squared difference Δm²₃₂ is one of the two precisely measured neutrino mass splittings. It is measured by studying how neutrinos produced in cosmic ray interactions in the atmosphere oscillate as they travel through the Earth. This paper derives it from the 600-cell spectral geometry. The result connects the neutrino mass scale to the same eigenvalue structure that produces the proton mass and the fine structure constant — confirming that the neutrino sector is part of the same algebraic framework.