  We present a symmetry-preserving scheme to derive the pion and kaon
generalized parton distributions (GPDs) in Euclidean space. The key to
maintaining crucial symmetries under this approach is the treatment of the
scattering amplitude, such that it contains both the traditional leading-order
contributions and the scalar/vector pole contribution automatically, the latter
being necessary to ensure the soft-pion theorem. The GPD is extracted
analytically via the uniqueness and definition of the Mellin moments and we
find that it naturally matches the double distribution; consequently, the
polynomiality condition and sum rules are satisfied. The present scheme thus
paves the way for the extraction of the GPD in Euclidean space using the
Dyson-Schwinger equation framework or similar continuum approaches.
