This is an interesting preprint, and it got me captivated for several minutes. First of all, let's set the scenario.
In the periodic table, as one go from H to higher numbered atoms, one start filling up various atomic orbitals. So you have H having 1s^1, He with 1s^2, Li with 1s^2 2s^1, etc.. etc. The interesting thing here is that with just the electron-ion interaction being accounted for, the 2s and 2p states in Li are degenerate, meaning they both have the same energy. So why would the 2s state gets filled first ahead of the 2p?
The standard textbook explanation here is that the 2p states, due to the geometry of the orbitals, tend to get shielded more by the 1s electrons than the 2s states. Thus, the 2p states have a higher energy than the 2s states.
This preprint claim that that explanation is flawed. They showed that what is really at play here is the electron-electron interaction, which is often neglected in many of these multi-electron systems with low atomic number. In their calculation, the interaction between 1s - 2s electrons produced a lower energy state than the interaction between 1s - 2p electrons. This is the main reason for Li ground state to be what it is, and not due to "shielding".
I'm sure this is being submitted for publication somewhere. The paper is not that difficult to follow for advanced undergraduate physics students.