Since Robau knew what stardates were, and used one based on the Gregorian calendar, I suppose it would have to be either that system, or one that features figures lower than those used in TOS, so the aforementioned 3-digit system seems to make sense.
I dislike the Gregorian-based stardate system for the simple reason that it's extremely Earth-biased in a Federation society that's supposed to embrace other worlds. On my initial viewing of the 2009 film, it was actually the thing that stuck out the most to me. One reason I like the stardates is that they provide something universal to consolidate the calendars of countless worlds.
But while I don't like Gregorian-based stardates, I do think I prefer ignoring Robau's knowledge of stardates and using the Earth dates as ENT did, showing an early Federation system that perhaps either sectioned off Earth dates for Starfleet, or for ships captained by Earth natives, or some such other reason. It would be easier than coming up with a fourth or fifth system of stardates (after the 4-digit/1000 units a year in TOS, 4-digit/100 units a year in the TOS movies, 5-digit/1000 units a year from the TNG era, and the 4-digit, day-based decimal/Gregorian-centric system of the Kelvin timeline).
Whatever they do, if they have logs, I hope they actually say the date instead of saying "supplemental." "Supplemental," is fine if there's more than one log in a mission, but the initial entry should state the date.
