  We consider the problem of bounding CFT correlators on the Euclidean section.
By reformulating the question as an optimization problem, we construct
functionals numerically which determine upper and lower bounds on correlators
under several circumstances. A useful outcome of our analysis is that the gap
maximization bootstrap problem can be reproduced by a numerically easier
optimization problem. We find that the 3d Ising spin correlator takes the
minimal possible allowed values on the Euclidean section. Turning to the
maximization problem we find that for d > 2 there are gap-independent maximal
bounds on CFT correlators. Under certain conditions we show that the maximizing
correlator is given by the generalized free boson for general Euclidean
kinematics. In our explorations we also uncover an intriguing 3d CFT which
saturates gap, OPE maximization and correlator value bounds. Finally we comment
on the relation between our functionals and the Polyakov bootstrap.
