  The muon anomalous magnetic moment continues to attract interest due to the
potential tension between experimental measurement [1,2] and the Standard Model
prediction [3]. The hadronic light-by-light contribution to the magnetic moment
is one of the two diagrammatic topologies currently saturating the theoretical
uncertainty. With the aim of improving precision on the hadronic light-by-light
in a data-driven approach founded on dispersion theory [4,5], we derive various
short-distance constraints of the underlying correlation function of four
electromagnetic currents. Here, we present our previous progress in the purely
short-distance regime and current efforts in the so-called Melnikov-Vainshtein
limit.
