Here is a proof of concept screenshot which shows that he has managed to successfully run arbitrary code on the 05.11.07 baseband.
For those of you who don’t know, geohot is the guy who first unlocked the original iPhone in 2007, and then later he was the first one to provide all-in-one jailbreak solution for iPhone 3.1.2 firmware through his infamous tool, named blackra1n.
If your phone is on 05.11.07 baseband with 05.08 (5.8) Bootloader from factory, then follow our guide here to downgrade your baseband from 05.11.07 to 04.26.08 in order to jailbreak and unlock it on iPhone 3.1.2 firmware.