Rigorous convergence and solver-error certification

Prove a general convergence theory for the Stieltjes bootstrap and establish an a posteriori certification of its bounds that accounts for numerical errors introduced by the semidefinite-programming solver.

Background

The paper reports exponential convergence of the bootstrap bounds in its principal examples, while noting that algebraic convergence or failure to converge can occur depending on the homogeneous solutions of the differential-equation system. It also describes exact post-processing of numerical dual certificates, but does not provide a general theory covering convergence rates or certification against all numerical solver errors. These two issues are explicitly identified as unresolved directions.