  We describe the twisted doubling integrals of Cai-Friedberg-Ginzburg-Kaplan
in a conceptual way. This also extends the construction to the quaternionic
unitary groups. We carry out the unfolding argument uniformly in this article.
To do so, we define a family of degenerate Whittaker coefficients that are
suitable in this setup and study some of their properties. We also prove
certain related global and local results that use the same tools.
