  We present predictions for the gluon-fusion Higgs $p_T$ spectrum at
N$^3$LL$'$+N$^3$LO order 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.
