Although our concrete hearth will be about a foot thick, it will appear to “float” above the floor.This bit of optical trickery will be achieved by a 5 inch indentation at the bottom of the form  created using ridged foam.  After the concrete has set, we will remove the foam.  We will also be lining the upper inside edge of the form with a continuous band of metal flashing.  This should give us a perfectly smooth “face” on the hearth which will be a nice contrast with the exposed aggregate top surface.   Thanks to Jeff for the inspiration to create the floating concrete effect.
The black pipe sticking out of the floor is for bringing in combustion air for the wood stove from the outside . (rather than creating a draft through doors and windows)