  The microscopic theories of quantum gravity related to integrable lattice
models can be constructed as special deformations of pure gravity. Each such
deformation is defined by a second order differential operator acting on the
coupling constants. As a consequence, the theories with matter fields satisfy a
set of constraints inherited from the integrable structure of pure gravity. In
particular, a set of bilinear functional equations for each theory with matter
fields follows from the Hirota equations defining the KP (KdV) structure of
pure gravity.
