Heavy-Quark Pair Production at Lepton Colliders at NNNLO in QCD.

We compute the total cross section and invariant mass distribution for heavy-quark pair production in e^{+}e^{-} annihilation at the next-to-next-to-next-to-leading order in QCD. The obtained results are expressed as piecewise functions defined by several deeply expanded power series, facilitating a rapid numerical evaluation. Utilizing top-pair production at a collision energy of 500 GeV as a benchmark, we observe a correction of approximately 0.1% for the total cross section and around 10% for the majority of the invariant mass distribution range. These results play a crucial role in significantly reducing theoretical uncertainty: the scale dependence has been diminished to 0.06% for the total cross section and to 5% for the invariant mass distribution. This reduction of uncertainty meets the stringent requirements of future lepton colliders.