  Building upon the PDFSense framework developed in Ref. [1], we perform a
comprehensive analysis of the sensitivity of present and future high-energy
data to a number of quantities commonly evaluated in lattice gauge theory, with
a particular focus on the integrated Mellin moments of nucleon parton
distribution functions (PDFs), such as $\langle x \rangle_{u^+ - d^+}$ and
$\langle x \rangle_{g}$, as well as $x$-dependent quark quasi-distributions --
in particular, that of the isovector combination. Our results demonstrate the
potential for lattice calculations and phenomenological quark distributions
informed by high-energy experimental data to cooperatively improve the picture
of the nucleon's collinear structure. This will increasingly be the case as
computational resources for lattice calculations further expand, and QCD global
analyses continue to grow in sophistication. Our sensitivity analysis suggests
that a future lepton-hadron collider would be especially instrumental in
providing phenomenological constraints to lattice observables.
