N3LO quadratic-in-spin interactions for generic compact binaries

We derive the third subleading (N$^3$LO) corrections of quadratic-in-spin sectors via EFT spinning objects in post-Newtonian (PN) gravity. These consist contributions from $4$ for generic compact binaries, that enter at fifth PN order. One these is due to a new tidal interaction, unique with spin, and complements first interaction also enters this order simple point-mass sector. The evaluation Feynman graphs carried out dimension advanced multi-loop methods, gives rise dimensional-regularization poles conjunction logarithms. At higher-spin reduction generalized Lagrangians entails redefinitions position beyond linear provide here most general Hamiltonians. then specify latter simplified configurations, consequent gauge-invariant relations among binding energy, angular momentum, frequency. end derivation all scattering angles correspond an extension our Hamiltonians problem aligned-spins configuration, as guide scattering-amplitudes studies.