Tell me if I've got the basics straight:

[Wacky Willy]

AI controls the entire galaxy, player starts with only one system under siege.

AI periodically sends waves against the player and reinforcements to planets adjacent to detected player systems.

AI also has special forces bases.  Ships reinforcing the special forces bases patrol between other special forces bases.  Astro train stations work similarly

AI command stations make reinforcements possible in a system, including command posts (side note: naming them command posts is confusing.  Suggest renaming them with something that doesn't have the word "command" in it).  If a warp gate is destroyed, but the command station left alone, the warp gate is not replaced by reinforcement.  Destroying the command station has a 50% chance of causing forces defending command posts to stop defending and attack player systems.

The penalty for a player turtling their initial system until they have a fleet at their unit cap is that all the adjacent planets will have much stronger fleets defending them due to reinforcement waves.

Did I miss anything?  Is there any circumstance under which the AI attacks planets other than waves, being in the path of a Special forces or Astro train route, or destroying command stations?

[x4000]

Pretty close.  All of that is generally accurate, but there are some omissions (and I'm not inclined to rename command posts at this time, unless there is a lot of support for that, but thanks for bringing it up).

1. Any time you destroy a command post or station, any ships that were guarding it will be "freed" and come after you, same as happens with the 50% chance after command station destruction.

2. Periodically the AI will build up devastating 1000 to 2000 ship cross-planet attacks.  These might come every 40 minutes or so, depending on your difficulty level.  These only come when a planet has enough ships to at least have 1000ish ships left after the attack sends ships your way.  So if you just turtle for a long time and build up more ships, you are also letting them reinforce all over the place and then you will have a harder time later with these cross-planet attacks.  Plus, you can't get much in the way of knowledge if you are just turtling, so your expansion is likely to all but cease which again can lead to your demise with the cross-planet attacks.

You could probably survive indefinitely just by turtling, but that's like saying that you can survive at the start of a Mario Galaxy level for as long as you want.  You won't be making much progress, since probably the AI is making progress at least on par with you while that is happening.