Year: 2026
Type: preprint
Abstract: We give an exact counterexample to the eight-point angular-energy conjecture stated by Mouchet in 2005 and published in 2006. The conjecture specifies both a radical value for the global maximum and a square antiprism with unit-side horizontal squares separated by $h_0=\sqrt{1+2\sqrt{2}}/2$. We prove that the same family at the rational separation $489/500$ has a strictly larger angular sum. The proof reduces the sum of all $168$ angle cosines to a one-variable formula, factors its derivative, and certifies its sign using rational inequalities. We also characterize the unique maximizing separation within this family. All comparisons needed for the counterexample are exact. The result disproves the exact stated conjecture.
Source: arXiv (Cornell University)
Author: Zhao, Jinze
Institution: University of California San Diego
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220408801