Static Equilibria of Perturbed Spheres: A Single-Harmonic Class Map, a Parity Obstruction, and a Certified Counter for the Mono-Monostatic Regime

Vincent Wesley Couey

Varkonyi and Domokos proved that homogeneous convex bodies exist with any prescribed numbers $S\ge 1$ of stable and $U\ge 1$ of unstable static equilibria, the case $S=U=1$ being the…