which boxes have been opened, which houseplants have been farmed, etc.) even very far away from one's current position, but I don't know what its limits are, and I would be very surprised if it remembers that info after the game has been shut off.
The game seems to do a good job of remembering the state of things (e.g. If you set your ship down right next to a crashed one (so you can easily find your ship again), then you can claim ownership of the crashed ship, scrap all of its parts for valuable elements, and walk over and reclaim ownership of your original ship.