  We complete the analytical determination, at the 4th post-Newtonian (4PN)
approximation, of the conservative dynamics of gravitationally interacting
two-point-mass systems. This completion is obtained by resolving the infra-red
ambiguity which had blocked a previous 4PN calculation [P.Jaranowski and
G.Sch\"afer, Phys. Rev. D 87, 081503(R) (2013)] by taking into account the 4PN
breakdown of the usual near-zone expansion due to infinite-range
tail-transported temporal correlations found long ago [L.Blanchet and T.Damour,
Phys. Rev. D 37, 1410 (1988)]. This leads to a Poincar\'e-invariant
4PN-accurate effective action for two masses, which mixes instantaneous
interaction terms (described by a usual Hamiltonian) with a (time-symmetric)
nonlocal-in-time interaction.
