I like seeing something that isn't a module in here. That said, I'm not sure it fits the jam's theme at all. Maybe it's just something you were working on anyway and decided to participate, which is fine, but it means I can't give a good rating for Theme even though I like the idea.
I would include early on a one-sentence literal description of what a Generation Ship is, perhaps instead of or just before "a sci-fi tradition representing the indomitable human spirit." I think that most people are familiar with the basic idea of them but might not know that's the term for it.
The first few tables are fine, but I'm not sure I like the lengthy narrative procedure for detailing the ship's entire history. I guess it works as a solo game for people who really love just chucking some dice and I see that some other commenters are into that, so it's probably just a personal preference thing.
Personally, I would rather just roll once for the ship's current status, then one or more times to see the current crisis and/or past issues it has overcome, etc. That would then leave some space to generate details about its layout and technological capacities, which IMO is more important than the full history if we're planning on running an adventure on board.
I think the example on the back panel is much too long. It would probably be better to show just a few "steps" on the journey, after which the reader gets the basic idea. I doubt many people are going to follow step by step through that entire wall of text, and it's redundant after the first few. If you cut it down by 50% or more, you could use the rest of the back panel for something else, e.g. maybe four little schematics showing how the modules might be arranged for basic Generation Ship archetypes, for Wardens who need some help getting started on their maps.
Small wording note: I'd replace "disabled" with "damaged" because if Life Support or Agriculture were actually disabled, everyone would just be dead, and your intent seems to be that "disabled" modules are just not working at 100% anymore.
Anyway, aside from the thematic non sequitur, my only big criticism is a matter of preference. In terms of accomplishing what you set out to accomplish, it seems like a functional set of rules.