The longshot is a Bussard Ramjet spine, kilometers long, with four free-fall habitats mechanically mounted in pairs along its core. Each habitat is a functioning colony, with its own freefall industries, living and recreation areas, courier and shuttle vessels, intrasystem lightsail, and so on... each operates in a low-power mode fed by the longshot's fusion flame, and only needs to be released at a low velocity (the Ramjet taking advantage of incoming solar wind to drop below interstellar lightsail speed long enough to do the drop) to function independently.
This longshot has for some perverse reason been brought to mere orbital velocity in the trojan point of a habitable system. Presumably the habitats would have been expected to build a launch laser to kick it back up to intersteller speed. Unfortunately, the habitats and starship have been abandoned, the ships AI (a crippled primitive one, barely deserving of the name) and one crew-pack (Argent) maintaining the life-support in one small sealed-off part of one of the four habitats.
Argent believe the longshot is real, and spends most of their time there. The timeslips that occasionally strand them outside the flow of time, so months pass while Puzzlebox changes not at all, or isolate the longshot for weeks of outside time while nothing passes within, well, they can probably be explained without invoking time travel. Causality isn't all it's cracked up to be, after all.