A PSI Core is an item that can only be acquired by purchasing it at the camp store in the Main Lodge at Whispering Rock Psychic Summer Camp. They cost 10 arrowheads. Combining them with nine PSI Cards, which are found floating all over the real world, allows the player to cash in on a PSI Challenge Marker, which increases their PSI Cadet Rank by one level. The place you need to go to mix these with the PSI cards and get a rank is Ford's Sanctuary. Razputin can travel there using the fast travel underground mine carts scattered around the overworld.