We consider a free Klein-Gordon field in a space-time equal to the interior of some  past light cone. Quasi-free states inside the cone can be constructed from quasi-free states for some CCR algebra of functions on the cone itself. We give a large class of states on the cone inducing Hadamard states inside the cone, using pro calculus on the cone. We prove that pure states in this class induce pure states in the bulk. (Joint work with Michał Wrochna).