Complete four-loop pressure of cold QED

Extending the weak-coupling expansion of the pressure of a cold and dense ultrarelativistic electron gas to next-to-next-to-next-to-leading order (N3LO) in the gauge coupling has remained an open problem since the classic N2LO result of Freedman and McLerran, published in 1977. Here, we present the full N3LO pressure, the first thermodynamic quantity determined to this order in a physical gauge theory. The pressure exhibits good perturbative convergence and weak renormalization-scale dependence even at sizable couplings, while a Bayesian analysis of missing higher-order contributions indicates uncertainties that can exceed those inferred from scale variation alone.