Year: 2026
Type: preprint
Abstract: 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 proper-line construction has at least two nondegenerate minima but only one relatively effective zero-dimensional cell intersection. For each positive subspace dimension, product suspension gives a proper-subspace counterexample.
Source: arXiv (Cornell University)
Author: Duan, Xiuqing
Institution: Nanyang Technological University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212127324