Having more knowledge of theoretical physics, artificial intelligence, and human consciousness than everyone else in the now-annihilated solar system combined, the REFOLA team was in a position to deduce approximately what had happened.

1. The emergency system activated the AI, which was directly responsible for pretty much everything that happened.
2. The AI figured out the situation and decided to save as many humans as possible.
3. The AI harnessed the power of the supernova to act as quickly as possible.
4. The AI solved enough of the problems of cross-dimensional travel to send the humans to another, hopefully safer, dimension.
5. Either the AI made an impossibly lucky guess about where to send the people, it was able to scan the possible choices in advance, it sent an entire world with the humans, or it copied the humans and sent copies to as many places as possible. By definition "impossibly lucky" is impossible, but in this sort of situation only the impossibly lucky survive to note how impossible their luck is. Scanning is plausible, but the apparent inability to send electronic devices intact would severely limit the extent of the scans. Theoretically, there was enough energy in the supernova-ing sun to generate an entire planet and a smaller sun, but earlier cross-dimensional research indicated that transmitting such large objects to another dimension would use too much energy. There was no consensus on this issue.
6. The AI intentionally skipped sending the electronic devices with the humans for an unknown reason. Perhaps the sending process would corrupt them, or maybe the AI calculated that humanity would fare better overall without keeping the old technology. Either way, the REFOLA team would rebuild and gain an unsurpassable lead in technological redevelopment.
7. The cross-dimensional sending process caused the partial amnesia and disorientation in everyone, and the AI drugged everyone not on the REFOLA team such that they would more readily accept their new world and forget about the old one.
8. The glowing stones convert heat to light, explaining why they're always cold and glow more when touched by (relatively warm) people.
9. The anti-gravity stones convert water into energy to generate the anti-gravity fields.
10. At minimum, the AI was able to make the giant glowing word REFOLA and was probably responsible for most of the cave system in general.

Everything was speculative, but the cases where the AI seemed to have made intentional choices with its superior information gave clues about what it planned for the REFOLA team to do.

Next: What to do