  We propose a "locally-smeared Operator Product Expansion" (sOPE) to decompose
non-local operators in terms of a basis of locally-smeared operators. The sOPE
formally connects nonperturbative matrix elements of smeared degrees of
freedom, determined numerically using the gradient flow, to non-local operators
in the continuum. The nonperturbative matrix elements do not suffer from
power-divergent mixing on the lattice, provided the smearing scale is kept
fixed in the continuum limit. The presence of this smearing scale prevents a
simple connection to the standard operator product expansion and therefore
requires the construction of a two-scale formalism. We demonstrate the
feasibility of our approach using the example of real scalar field theory.
