I've asked around at local stores and they had no idea what it was.
A ceramic part in the valve broke so I can't just pick up a generic o-ring.
The stem has 16 teeth and 0.4" 0.365" diameter.
The valve is 5 inches long.
Best Answer
I found a brand on the sinks that are the same style. The company that made the faucet appears to be Harden. The style of the cartridge has similarities to others I'm seeing online for Harden.
Two for the price of one, first section is how to replace the seat washer, second to repair stem leakage.
Note: The Handle, Stem, Stuffing Box, Packing Nut, Packing Nut Seal and Seat Washer all come out as one complete assembly on this faucet.
Replacing the Seat Washer, Faucet leaks when fully closed.
Find the water shutoff for the zone this faucet is in (mains for whole house if that's the only one) and shut the water supply off.
Turn the hose bib handle 1/4 turn open.
Loosen the Packing Nut (see illus below). As you turn it, the Stem will probably turn with it, if not, turn both Stem and Packing Nut in the same direction till the Stem/Packing Nut assembly comes out of the faucet body.
Remove the Seat Sealing Washer screw, and replace the washer.
Reverse operation for assembly.
If the faucet is leaking around the handle, gently tighten the Stuffing Box Nut 1/16-1/8 turn to compress the packing (what the stem seal is called). If it feels like you're tightening metal to metal, the packing has worn out and needs to be replaced.
Replacing the Packing, Faucet leaks around the stem when open.
Remove Handle Screw and Handle.
Remove Stuffing Box Nut (also called a Gland Nut).
Remove Packing and replace with new packing washer or graphited packing cord.
Replace Stuffing Box Nut (finger tight)
Replace Handle and Handle Screw.
Make sure you have a hose and closed nozzle attached to the hose bib.
Open faucet to pressurize hose and tighten Stuffing Box Nut down gently until the stem stops leaking.
As Steven says, hit it with some penetrating oil first (WD-40 should work for this). Give it some gentle whacks against a piece of scrap wood in all directions to help break any bonds. Then clamp on to the bottom square part and try to torque the nut on top with a socket. If you still can't get it, you may find it easier to replace the entire thing.
Best Answer
I found a brand on the sinks that are the same style. The company that made the faucet appears to be Harden. The style of the cartridge has similarities to others I'm seeing online for Harden.
The part appears to be "harden 185"