My bathroom sink faucet has seized up and needs replacement. It should be a simple swap of a new cartridge. But I can't figure out the brand! The faucet is likely 20 years old and may be as old as 40 years. The sink itself is labeled Kohler. The ribbed spline on top has 16 ridges. Yet the exposed cartridge does not look like the common Kohler cartridge type... especially the ribbed top with the two sections. There's no label or printing on the stem.
To be honest I haven't seen one like this but the simplest solution would be to turn off the water to it, should be a valve under the sink and remove the valve stem. The first hex nut above the large thread, turn counter clockwise, once out take it to a plumbing supply to match it with a replacement new one and install it to get things working again.