GeoHot will not update blackra1n to support firmware 3.1.3
GeoHot recently posted a small message on twitter. He actually responds to many users who continue to ask him about the ability to run firmware 3.1.3 jailbreak using Blackra1n.
GeoHot has always been a bit reluctant to release new versions for various minor firmware updates. His advice is in fact once again to keep firmware 3.1.2, because the latest one does not have anything interesting.
GeoHot will be certainly back on the scene with the next release of firmware 3.2 in March / April or firmware 4.0 that is expected in July.