  We study higher form Proca equations on Einstein manifolds with boundary data
along conformal infinity. We solve these Laplace-type boundary problems
formally, and to all orders, by constructing an operator which projects
arbitrary forms to solutions. We also develop a product formula for solving
these asymptotic problems in general. The central tools of our approach are (i)
the conformal geometry of differential forms and the associated exterior
tractor calculus, and (ii) a generalised notion of scale which encodes the
connection between the underlying geometry and its boundary. The latter also
controls the breaking of conformal invariance in a very strict way by coupling
conformally invariant equations to the scale tractor associated with the
generalised scale. From this, we obtain a map from existing solutions to new
ones that exchanges Dirichlet and Neumann boundary conditions. Together, the
scale tractor and exterior structure extend the solution generating algebra of
[31] to a conformally invariant, Poincare--Einstein calculus on (tractor)
differential forms. This calculus leads to explicit holographic formulae for
all the higher order conformal operators on weighted differential forms,
differential complexes, and Q-operators of [9]. This complements the results of
Aubry and Guillarmou [3] where associated conformal harmonic spaces parametrise
smooth solutions.
