ζ is a particle that attracts other ζs, but since logic can destroy ζs, it repels all things that can contain it, like α.
If this particle collides with another ζ, then a new ζ will be born, but the two ζs that collided will temporarily not exist (this lasts for 10 seconds). If the α exists, and contains the ζs, then the ζs will rush out, forming a few groups out in β.
One of ζ's purposes is to contain vacuums, as vacuums can contain ζ, so ζ repels it. If ζ is contained within a thick α, then the ζ won't drift away, allowing vacuums to not drift away. This is an important part of the Logicsphere.
Another of ζ's purposes is to phase through barriers. You have to hit yourself with 1 googolplexian meter of force per centimeter in your body, then the ζs inside will harness the force, due to the Logicsphere being broken. This can allow you to stop existing for 10 seconds, allowing phasing through anything. However, external forces are needed to push you in this timeframe, or you won't be able to phase.