Hearth Cap stone

We just built a new addition with a bump out for a propane fireplace. As you can see in this picture, the entire bump out and hearth have zip system sheathing for the floor.


Now that the fireplace has been installed there are 2 issues which come to light regarding the top of the hearth.

First, can the hearth cap stone be mortared onto zip system sheathing? There is not enough space to attach cement board over the sheathing and then fit 1" stone.

If the answer to my first question is no, my next thought was to remove the sheathing right up to the stove (this will be a challenge), and replace it with cement board. In this scenario the cement board will be affixed directly to the hearth framing. Can the cement board withstand the weight of somebody sitting on he hearth without sheathing underneath?

 

How large and heavy is the stone? If it's one slab and decently heavy you could just let gravity hold it in place. A step up you could use construction or another adhesive to glue it in place. I've never tried mortaring to Zip so that would not be my first choice as mortar generally doesn't stick well to wood.