  The asymptotic safety conjecture is examined for quantum gravity in four
dimensions. Using the renormalisation group, we find evidence for an
interacting UV fixed point for polynomial actions up to the 34th power in the
Ricci scalar. The extrapolation to infinite polynomial order is given, and the
self-consistency of the fixed point is established using a bootstrap test. All
details of our analysis are provided. We also clarify further aspects such as
stability, convergence, the role of boundary conditions, and a partial
degeneracy of eigenvalues. Within this setting we find strong support for the
conjecture.
