3 problems

Incompressibility conjecture. The lower bound for the ground-state energy should satisfy

General-potential Laughlin trial-state conjecture. A suitable trial state can always be constructed in the form of the Laughlin ansatz $\Psi_{\rm Lau}$.

Full-kernel optimality conjecture. The restriction to states built on $\mathcal{V}_2^D$ is unnecessary: the same asymptotic optimality result holds when the full variational set…