Optimal selection of Stieltjes integrals for the bootstrap

Determine the optimal selection of Stieltjes integrals to impose as positivity constraints in the Stieltjes bootstrap, balancing the accuracy of the resulting enclosures against the computational cost of the semidefinite programs.

Background

For the three-loop two-mass ladder family, the authors construct 149 scalar Stieltjes integrals while the family has 60 master integrals. Using all 149 integrals improves the numerical bounds but substantially increases semidefinite-programming cost; using only a smaller set would likely be faster but could weaken the feasible region. The optimal choice of constraint integrals is therefore left unresolved.