Abstract We compute the N3LO gravitational quadratic-in-spin interactions at G 4 in the post-Newtonian (PN) expansion via the effective field theory (EFT) of gravitating spinning objects for the first time. This result contributes at the 5PN order for maximally-spinning compact objects. adding the spinning case to the static sector at this PN accuracy. This sector requires extending t... https://www.nacrack.com/