I think you're not fully understading the theory of the Boltzmann brain. A Boltzmann brain would not exist for any extended period of time. They only exist fo

I think you're not fully understading the theory of the Boltzmann brain. A Boltzmann brain would not exist for any extended period of time. They only exist for an instant, they don't "track" any sort of existence or conciousness, they merely pop in to existence for an instant and then disappear the next. Imagine your current mental state as a snapshot. By pure luck some atoms could arrange into the exact same state as your brain is right now. And for that moment, it would be you, it would have your full set of memories. It would be indistinguishable from your current existence. And then the next moment it would cease to exist. But there could be infinite many such brains popping in to existence and then disappearing at every instant, with every conceivable configuration of state/memories.