About 25-30 psi. Flatter tread patch was at like 21 psi. The 12.50s are really rounded on an 8" wheel. If you check out the early photos you can see it. This size really needs to be on a 10" wheel.
Wet pavement traction was outstanding, like just wet, what wasn't impressive was pooling water in rutted pavement.
We have good paved 2 laners in my county but they get a lot of heavy truck traffic from the farmers so they are badly rutted with the occasional 2"+ puddle. You hit any water deeper than about a half inch with this tire in this size and watch out. If you see it coming you can just veer around the rut or puddle a bit.
It's true the sipes are great, but the tread design is such that water can just squirt out of the tread. This was not an issue in the narrower size we ran on our 1 ton. But 12.50 wide this tread will hydroplane.
If you are running 31x10.50s I'll bet they won't have this problem at all.