Given that it's several decades since I last competed in a TT I've rather lost touch with who certifies what for time/distance records. 10 minutes googling reveals that, as mattc aludes to, there are records and records, depending on who's list you look at:
Guinness World Records has 903.76km (561.57 miles) by Marko Baloh (Ch) as the absolute record but that was on a 250m velodrome (8-9 Oct 2010)
UMCA unpaced road record 521.975 miles (839.39km) Jure Robic 2004
CTT/RTTC Andy Wilkinson 541.17 miles (870.93km) 2011
RRA Gethin Butler 505.8 miles (840.04km) 2001
I presume the present go would resemble an RRA attempt.