Computing spectral properties from Euclidean data without assumptions

Spectral functions encode the real-world dynamics of quantum fields, but extracting them from numerical simulations requires assumptions that can bias results. This work develops a method to compute guaranteed upper and lower bounds on spectral observables directly from Euclidean lattice data, optimizing over all possible spectral densities consistent with the measurements. The approach converts the problem into a semidefinite program—standard optimization that doesn't require guessing the spectral shape.