  A recent paper [Lee {\em et al.}, J. Korean Cryt. Growth Cryst. Techn. {\bf
33}, 61 (2023)] provides some experimental indications that
Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O with $x\approx 1$, coined LK-99, might be a
room-temperature superconductor at ambient pressure. Our density-functional
theory calculations show lattice parameters and a volume contraction with $x$
-- very similar to experiment. The DFT electronic structure shows Cu$^{2+}$ in
a $3d^9$ configuration with two flat Cu bands crossing the Fermi energy. This
puts Pb$_{9}$Cu(PO$_4$)$_6$O in an ultra-correlated regime and suggests that,
without doping, it is a Mott or charge transfer insulator. If doped such an
electronic structure might support flat-band superconductivity or an
correlation-enhanced electron-phonon mechanism, whereas a diamagnet without
superconductivity appears to be rather at odds with our results.
