Former physicist here. Your speculation about path integrals and measure theory isn't quite right. Lattice QCD methods are definitely proven to be equivalent t

Former physicist here. Your speculation about path integrals and measure theory isn't quite right. Lattice QCD methods are definitely proven to be equivalent to the continuum theory when you take the appropriate limits. This isn't some mathematical mystery - Wilson's groundbreaking work in the 70s established this, and it's been rigorously developed since. The actual g-2 puzzle is much more straightforward: we have competing measurements from different sources: 1. The Fermilab Muon g-2 experiment in Illinois directly measured the muon's anomalous magnetic moment. 2. The "data-driven" prediction used e+e- collision measurements from various experiments (BaBar at SLAC, KLOE in Italy, etc.) to calculate what the Standard Model predicts for g-2. This initially disagreed with Fermilab's measurement. 3. Lattice QCD calculations (like those from the BMW collaboration) produced theoretical predictions that matched Fermilab's experimental result. 4. More recently, new e+e- measurements from the CMD-3 experiment at VEPP-2000 in Russia (2023) are bringing the data-driven approach closer to both the lattice calculations and Fermilab's experimental values. So it's really just a question of which experimental measurements of e+e- collisions are most accurate/resolve any experimental differences, not some exotic mathematical issue with QFT formulations.