The Cognitive Reactor is what converts the knowledge you have mastered in game into energy which you need in game to perform the various activities on the world map, everything from exploration to attacking(using Storms) against enemy cities and oracles.  Like all buildings in game the Cognitve Reactor has five levels.

Cognitive Reactor Chart
Level Max Energy Max Pop Increase Shield Size Shield Strength Genium Cost
1 250 1200 5 1
2 750 400 10 2
3 1500 600 15 3
4 3000 800 20 4 40000
5 6000 1000 25 5 80000

Up to and including Closed Beta 3.2 the Brain Knowledge Fragment was earned by building the Cognitive Reactor Level 1.

Up to and including Closed Beta 3.2 Max Energy at level 5 was 5000, this was increase to 7000 for Closed Beta 4.0, then decreased again to 6000 for Closed Beta 4.2.

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