Historically your chances of popping a bead start to really climb as you get below 20 psi. Now start playing in the rocks like the "slick" rock of Moab and I have see guys pop beads at 24 lbs...as the CoT (Coefficient of traction goes UP and psi goes down its a crap shoot.
I have seen some guys run 15 and get away with it, but it was more mud than hight traction dry ground or rocks.
It’s all variable. It depends on traction, wheel speed, wheel machining, tire bead, etc. I’ve run 8 psi in a 35x14.50 Super Swamper in a 10” wheel with no problem, and 12 psi in a 37x12.50 on a JK Moab wheel without issue. I’ve also seen guys with similar setups lose a bead, but is usually involved higher wheel speed and momentum.