The direct calculation of nucleon structure from first principles is an 
unsolved challenge for quantum chromodynamics (QCD). In particular, parton 
distribution functions (PDFs), which capture the longitudinal momentum 
structure of fast-moving nucleons, are defined on the light cone and are 
not directly accessible in Euclidean lattice QCD. To circumvent this 
problem, moments of PDFs can be expressed in terms of matrix elements of 
local operators, but these operators suffer from power-divergent mixing, 
which stems from the hypercubic symmetry of the lattice regulator. I will 
introduce a new method that suppresses this power-divergent mixing, at the 
expense of introducing a new physical scale in the continuum. I will 
highlight the role that this method plays in ab initio calculations of 
PDFs and outline a programme for the direct determination of nucleon 
structure on the lattice.