  We present the first analytic results of N$^3$LO QCD corrections to the
top-quark decay width. We focus on the dominant leading color contribution,
which includes light-quark loops. At NNLO, this dominant contribution accounts
for 95% of the total correction. By utilizing the optical theorem, the N$^3$LO
corrections are related to the imaginary parts of the four-loop self-energy
Feynman diagrams, which are calculated with differential equations. The results
are expressed in terms of harmonic polylogarithms, enabling fast and accurate
evaluation. The third-order QCD corrections decrease the LO decay width by
0.667%, and the scale uncertainty is reduced by half compared to the NNLO
result. The most precise prediction for the top-quark width is now 1.321 GeV
for $m_t=172.69$ GeV. Additionally, we obtain the third-order QCD corrections
to the dilepton invariant mass spectrum and decay width in the semileptonic
$b\to u$ transition.
