Maximum demonstrated is one of two things, and there's no easy way of telling which:-
(1) The maximum the test team could find during the certification flight test programme, and it was fine up to that, or...
(2) The test team went beyond that, but felt that this was a sensible maximum for pilots of average ability.
As for an absolute maximum, I'm not sure that such a term exists in the airworthiness regs. However, it is quite common for individual operators, be they airlines or flying clubs, to set a maximum permitted limit which they have decided is the greatest they want to see flown in their aircraft.
G