  The addition formulae for KP $\tau$-functions, when evaluated at lattice
points in the KP flow group orbits in the infinite dimensional
Sato-Segal-Wilson Grassmannian, give infinite parametric families of solutions
to discretizations of the KP hierarchy. The CKP hierarchy may similarly be
viewed as commuting flows on the Lagrangian sub-Grassmannian of maximal
isotropic subspaces with respect to a suitably defined symplectic form.
Evaluating the $\tau$-functions at a sublattice of points within the KP orbit,
the resulting discretization gives solutions both to the hyperdeterminantal
relations (or Kashaev recurrence) and the hexahedron (or Kenyon-Pemantle)
recurrence.
