A note on the Wu’s term in the ground state energy of a Bose gas in the Gross–Pitaevskii regime

We consider a gas of N interacting bosons in the three dimensional unit box in the Gross-Pitaevskii regime. We review the derivation of the third order correction for the ground state energy, of order log N/N, as obtained in Caraci et al., Commun. Math. Phys. 406, 153 (2025), explaining the key steps of the proof. In addition, we show how to obtain the optimal error term of order O(1/N).