As part of the basement remodel, the entire basement floor was covered with foam board and the joints spray foamed and sealed with Tyvek tape, then topped with 3/4" plywood screwed to the concrete so the hearth is being built on top of this. The basement walls are being spray foam insulated 2" deep. The back wall area behind the stove is not being foamed and that's the reason for the rigid insulation which is also sealed to continue the integrity of the 2" wall foam. Beyond the insulation value, creating a sealed thermal break will keep the basement relative humidity manageable in the warm months, and the stove won't have to warm all the concrete floor and walls in the heating season. The noncombustible area around the stove and stove pipe exceeds all the manufacturers requirements, and all the combustible material used to build the back wall and hearth will be covered in slate and stone. At this point I'm going to extend the 8" SS sleeve beyond the new back wall keeping all combustibles 6" away radially. I'll leave it to the installers to go from there when they come back to drop the liner in the chimney and re-install the stove on the new raised hearth