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).