  We present predictions for the gluon-fusion Higgs $p_T$ spectrum at third
resummed and fixed order (N$^3$LL$'+$N$^3$LO) including fiducial cuts as
required by experimental measurements at the Large Hadron Collider. Integrating
the spectrum, we predict for the first time the total fiducial cross section to
third order (N$^3$LO) and improved by resummation. The N$^3$LO correction is
enhanced by cut-induced logarithmic effects and is not reproduced by the
inclusive N$^3$LO correction times a lower-order acceptance. These are the
highest-order predictions of their kind achieved so far at a hadron collider.
