Completing the fifth PN precision frontier via the EFT of spinning gravitating objects

We put forward a broader picture of the effective theory spinning particle within EFT gravitating objects, through which we derive and establish new precision frontier at fifth PN (5PN) order. This includes higher-spin sectors, quadratic quartic in spin, both display novel physical features, due to extension beyond linear order curvature. The quadratic-in-spin sectors give rise tidal effect, quartic-in-spin exhibit multipolar deformation. then generalize concept operators spin-induced operators, make conjectures on numerical values their Wilson coefficients, point-particle action Kerr black holes. confirm generalized actions for generic compact binaries NLO were derived via objects. first present corresponding interaction potentials general Hamiltonians, consist 12 distinct with one These Hamiltonians full information binary system, mostly gets lost when going aligned-spins configuration. Moreover these uniquely allow us find complete Poincar\'e algebra 5PN spins, including third subleading sectors. consequent observables GW applications. Finally, contact scattering problem, also extrapolated angles aligned spins. Our completion provides strongest validation our most comprehensive results, thus that has now been established as frontier.