  We introduce a new technique for isolating components on the spectral side of
the trace formula. By applying it to the Jacquet--Rallis relative trace
formula, we complete the proof of the global Gan--Gross--Prasad conjecture and
its refinement Ichino--Ikeda conjecture for
$\mathrm{U}(n)\times\mathrm{U}(n+1)$ in the stable case.
