Anticipation was really good at the simulation of scenarios to find the best direction for the fleet as a whole. This might include figuring out what planets can be sustainable, or the literal physical direction the fleet should go. That job became dramatically more important in the last thousand years, with the decline of the Fleet.
The Divine's physical form and the ship itself is inspired by the funnels of the nu Gundam. It is formed of long rectangular floating pieces, which sit together in a fan shape or can spread out, forming shields in between them. There is no complete separation in this form, but they can form goal posts that create shields to protect other parts of the fleet: a much less elegant version of Thyrsus, comparatively. There are layers similar to a pocket knife that are still connected but can move. The body of the Divine itself, which died, is now considered the elevator between the different levels.
Anticipation decayed over time. Its ability to calculate slowed down to the point where it completely stalled, as though it's stuck in a rendering or buffering status. Before their death the ship's sections were able to fan out and signal or call to the other members of the fleet. Now they cannot, they can spin out a little bit, but they cannot perform that function.