punch 800a to a infinity 1052w

The other day i got the punch 800a from a buddy, didnt know anything about it so just took it and figured would find out later. I guess its 800 watts but i cant find anything online saying that to be true or not.  I also got the infinity reference 1052w really cheap from best buy so i figured i would go head and hook up some sort of system with the two since got them both cheap and before i go back to school.  We already ran all the wires and everything is ready to be plugged in. But given its a punch 800a and infinity reference 1052w can somone give me some sort of assurance on how to put all the wires into this particular setup? As in what ohm and load they need for both to perform properly.

Currently the sub is wired inside the box with option two on the link below. But that was with a different amp. I am not sure of anything about this punch 800a and the load its stable at and such. Do i have it right with option two still or do i need to change it up do to the different amp?

https://www.the12volt.com/caraudio/woofer_configurations.asp~Q~1~I~22

subwoofer specs: https://infinitysystems.com/car/products/product_detail.aspx?prod=REF1052W&cat=REF&ser=REF&Language=ENG&Country=US&Region=USA

Thanks alot guys just trying to get my wiring right before i blow something up

https://i39.photobucket.com/albums/e167/cory21/sub.jpg

Thats what ive come up with on how to wire it, atleast from everything ive looked up online and come to understand and all.  I dont feel as though its right but thats the exact way everything is setup, meaning thats what the amp looks like front and back and the headunit rca cables are run as well as the 'system remote control' wire which was run to the 'rem' piece of metal on the amp. So can anyone tell if im right or wrong or how to set it work?

Assuming you've chosen the correct output terminals for bridging (I don't remember if those are the right ones) then yes, your diagram will work.  Be sure to fuse the power wire connecting the amp to the battery at whatever is appropriate for the guage of wire you use (see the "Power and Ground" link in the left column.)

BTW, what is the "rem piece of metal" you refer to?

but the metal piece is where the red wire runs into and just hooks around it. Its just a piece of copper with a hole in it labeled REM.