Moments of parton distribution functions encode fundamental information about the quark and gluon structure of hadrons. Their determination in lattice QCD using standard local operators is, however, limited by renormalization and mixing problems, particularly for higher moments. I will discuss a new strategy based on local twist-two operators defined at positive gradient-flow time that resolves this theoretical obstruction and allows, at least in principle, the computation of PDF moments of any order. At nonzero flow time, these operators have particularly simple renormalization properties and can be constructed so as to avoid power-divergent mixing. This makes it possible to take the continuum limit at fixed physical flow time before matching to physical PDF moments in the continuum through the short-flow-time expansion. I will describe the flowed-local-operator framework and present numerical applications to pion and nucleon flavor non-singlet PDF moments, discussing the main statistical and systematic uncertainties, with particular emphasis on the continuum and small-flow-time extrapolations. These studies demonstrate the viability of the method and its potential to access higher moments that are difficult to determine with traditional local-operator techniques. In the non-singlet sector, where numerical results are currently available, preliminary projections indicate that the method could become competitive with global fits of experimental data. More generally, the framework is applicable beyond the non-singlet sector and provides a path toward a broader first-principles determination of hadron structure from lattice QCD.
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