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.
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