The AI Mainframe is a blue crystal that allows for the existence of manifested thoughts (i.e. "ghosts"/AI) including Chiyo, Sai, Shin, the Tracker, and a majority of the enemies. Both Shin (the mainframe itself) and Seto (Strange Blue Stone) have a part of it, which is why the latter can see manifested thoughts and experience memory items.
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While players don't know it at the time, the first time they run into the AI mainframe is when they receive the Strange Blue Stone from Grandpa. The full mainframe isn't shown until right before the final battle, where Shin takes it from the ceiling of the room where you first fight him and carries it with him to the top of Tokyo Tower. After Shin is defeated for the final time, he destroys it by throwing off the tower.
In the mangaEdit
Even though the mainframe is destroyed, Seto can still experience memory items because he still possesses the Strange Blue Crystal.