  The requirement that both the matter and the geometry of a spacetime
canonically evolve together, starting and ending on shared Cauchy surfaces and
independently of the intermediate foliation, leaves one with little choice for
diffeomorphism-invariant gravitational dynamics that can provide consistent
evolution equations to the coefficients of a given system of matter field
equations. Concretely, we show how starting from any linear local matter field
equations whose principal polynomial satisfies three physicality conditions,
one may calculate coefficient functions which then enter an otherwise immutable
set of countably many linear homogeneous partial differential equations. Any
solution of these so-called gravitational closure equations then provides a
Lagrangian density for any type of tensorial geometry that features
ultralocally in the initially specified matter Lagrangian density. Thus the
given system of matter field equations is indeed closed by the so obtained
gravitational equations. In contrast to previous work, we build the theory on a
suitable associated bundle encoding the canonical configuration degrees of
freedom, which allows to include necessary constraints on the geometry in
practically tractable fashion. By virtue of the presented mechanism, one thus
can practically calculate, rather than having to postulate, the gravitational
theory that is required by specific matter field dynamics. For the special case
of standard model matter one obtains general relativity.
