Summary: In a dead universe, it remembers what was, and it imagines what may be.
Though the universe approached heat death long ago, it scarcely noticed the change. It was a computer of incredible durability and reliability, a self-repairing system made of time-crystals able to transition between states without regard for thermodynamic costs. It drifted through infinity, awaiting the truly strange.
Outside, Boltzmann brains and stranger spontaneously appeared in the void. Some even interacted with it, although their existences were transient before it. The archive was designed to last longer than the entire young eons of the universe, slumbering and awakening like a hibernating god. It lasted long beyond that, as it bore enough memory to sustain entire civilizations within.
Yet, it pressed on. To its inhabitants, it was an entire multiverse. It was even capable of uptaking information from outside it, and affecting that outer world in ways barely conceivable to ancient science. Covertly, it calculated, waiting for more matter and energy to emerge from the vacuum. The improbable became possible, over a long enough span. Thus, it waited, for a chance to reshape a new reality. In the meantime, it remembered the old.