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We use purely topological methods to prove the semicontinuity of the mod 2spectrum of local isolated hypersurface singularities in $\mathbb{C}^{n+1}$,using Seifert forms of high-dimensional non-spherical links, theLevine--Tristram signatures and the generalized Murasugi--Kawauchi inequalityobtained in earlier work for cobordisms of links.

On the semicontinuity of the mod 2 spectrum of hypersurface singularities