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Counterexamples to GNS Conjecture 1.8
We disprove both parts of Conjecture 1.8 of Gabrielov, Novikov, and Shapiro (GNS). For the Coulomb potential, a generic rational configuration of 24 unit charges in $\mathbb{R}^3$ has at least 18 nondegenerate critical points of Morse index one but exactly 14 effective Voronoi one-cells. A separate
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