Uniform moment bounds under weaker hypotheses

Determine whether weaker hypotheses than the derivative-domination certificates imposed in the convergence theorem still yield uniform moment bounds for feasible truncated eigenstate-bootstrap functionals.

Background

The paper proves convergence of the eigenstate quantum bootstrap for polynomial Schrödinger operators satisfying explicit sum-of-squares confinement and derivative-domination conditions. These conditions provide moment estimates uniform in the truncation order, which are then used to reconstruct a regular Schrödinger representation and establish convergence to the physical energy shell.

The authors note that the derivative-domination certificates may be restrictive and explicitly leave unresolved whether uniform moment bounds, and hence potentially the convergence argument, can be obtained under weaker assumptions. This is distinct from the separate observation that the compactness proof provides no quantitative convergence rate, which is not itself stated as an open problem with an explicit uncertainty marker.