Purely based on what we have on this thread, the first possible indication of 'difficulties' at 11:00?
I believe that the problems already started earlier. But during this 4 minutes, there was the total loss off control. The cabin VS warning would light up if the pressurization system is not able to maintain indicated cabin altitude, this either to a high rate of decent or ascent. I haven't ever stressed the A340 Level_D Sim that way. So i cannot really tell you how much V/S (positive or negativ) is necessary to force it. I recal some earlier statements, +/-1800. Well. I guess that was the moment were the aircraft was falling out of the skies and the reason why V/S was exceeded and why the cabin V/S popped up.
11:14 IMHO was the moment when the aircraft on its way down from 35'000ft broke up in parts. Thats when there was nothing to comminicate anymore by ACARS
ACARS unfortunatly is not telling us what happened in the minutes before loosing control.
Cheers
Martin