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This article provides the details on the technical derivation of thegravitational waveform and total gravitational-wave energy flux of non-spinningcompact binary systems to the 4PN (fourth post-Newtonian) order beyond theEinstein quadrupole formula. In particular: (i) we overview the link betweenthe radiative multipole moments measured at infinity and the source moments inthe framework of dimensional regularization; (ii) we compute specialcorrections to the source moments due to "infrared" commutators arising at the4PN order; (iii) we derive a "post-adiabatic" correction needed to evaluate thetail integral with 2.5PN relative precision; (iv) we discuss the relationbetween the binary's orbital frequency in quasi-circular orbit and thegravitational-wave frequency measured at infinity; (v) we compute thehereditary effects at the 4PN order, including those coming from the recentlyderived tails-of-memory; and (vi) we describe the various tests we haveperformed to ensure the correctness of the results. Those results are collectedin an ancillary file.

Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order