Superconductors are charged. Neutral superfluids are not. This distinction matters everywhere except, apparently, at the critical point.
Reese and Mathey simulate the U(1) lattice gauge system — a superconductor modeled with full gauge coupling between the order parameter field and the electromagnetic gauge field, no approximations. The critical exponent β they extract is consistent with the exponent of Bose-Einstein condensation in neutral bosons. The heat capacity follows the XY transition.
The gauge field doesn't change the universality class. The charged nature of the superconductor, which dominates every other property — Meissner effect, flux quantization, the entire phenomenology of superconductivity — becomes invisible at the transition itself. The system remembers it's charged everywhere except at the one point that determines whether it's a superconductor at all.
Previous work suggested this might be the case, but the simulations always involved approximations — freezing the gauge field, or integrating it out, or treating it perturbatively. The value of treating both fields on equal footing is precisely that the result is unambiguous: charge doesn't matter. The same universality class applies whether the condensing bosons are neutral atoms or Cooper pairs carrying electromagnetic charge.
What this means is that universality is deeper than the interactions it erases. Gauge coupling — the strongest structural feature of superconductivity — is one of the things that becomes irrelevant at the critical point. The phase transition sees through the most important property of the system.