A hierarchy of semidefinite programs provides rigorous bounds on spectral density functionals from Monte Carlo data subject to reflection positivity, converging to statistical error limits.
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The causal bootstrap computes rigorous bounds on smeared spectral functions from non-perturbative Euclidean data by optimizing over the convex set of compatible positive spectral densities and reducing dual problems to semidefinite programs for certain kernels.
A lattice QCD+QED strategy is outlined for calculating isospin-breaking effects in inclusive tau decays to support high-precision HVP contributions to muon g-2.
Derives analytic integral-transform formulae to extract continuum and smeared spectral densities from Euclidean correlators, with O(a^2) lattice convergence and rigorous bounds for finite-volume effects.
SVD truncation of the exp(-ωt) kernel reconstructs smeared spectral functions from lattice correlators with controlled uncertainties and approaches the Mellin transform in the continuum limit.
Alternative truncation-based procedure for smeared spectral density extraction from lattice correlators using SVD-style decomposition to decouple noise from signal.
Framework for exact and approximate kernel transformations between smeared spectral functions, including systematic error bounds computable from input data.
The updated SM prediction for the muon anomalous magnetic moment is 116592033(62)×10^{-11}, showing no tension with the experimental average of 38(63)×10^{-11}.