Pinned k-star distance sets of E have positive k-measure once dim(E) exceeds (n^{2}+nk+k)/(2n+1), via a weighted paraboloid Fourier-extension identity.
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From weighted paraboloid restriction to $k$-stars and distance graphs
Pinned k-star distance sets of E have positive k-measure once dim(E) exceeds (n^{2}+nk+k)/(2n+1), via a weighted paraboloid Fourier-extension identity.