Can every point of Wilson's adelic Grassmannian be obtained by Krichever construction of solutions to KP equations?

Igor Krichever introduced an algebro-geometric construction of solutions of KP equations starting from an algebraic curve with some additional data.

George Wilson introduced the adelic Grassmannian, which is a subspace of the Sato Grassmannian parametrizing all solutions to KP equations.

Question: can every point of Wilson's adelic Grassmannian be obtained by Krichever's algebro-geometric construction?

Yes - the adelic Grassmannian precisely parametrizes "rational solutions of KP", which are the Krichever solutions attached to rank 1 torsion free sheaves on cuspidal genus 0 curves -- i.e. curves with $$P^1$$ as their bijective normalization (or subrings of the field of rational functions). Its adelic (or factorization) nature is explained by keeping track of the finite subset of $$P^1$$ which is the location of the cusps - i.e. this space parametrizes "Hecke modifications" (Backlund transformations) supported at given points of $$P^1$$. This is stated as Corollary 5.21 in https://arxiv.org/abs/math/0212094 though I think was known to Wilson, Berest, Mulase and others.