There are numerous items in the game which can help the player throughout their various attempts at the game, most of which follow them for all subsequent playthroughs once they are obtained.
The Ixomen Sphere is an advanced device that can do a variety of things from hovering and following its owner, essentially serving as a web browser, and various other less useful tasks. Lorem's roommate, Ipsum, lost his sphere and they can be found discussing it during one of Lorem's dates in his apartment.
The item can be found during the second investigation in Tatsu park. It is important in Lorem's story, but is useless without its charging base.
The charging base to the Ixomen sphere which enables it to be charged and made useful during Lorem's story. It can be found within the trash can in the police archives during the third investigation.
Note: If the player does not retrieve it from the police archives during the third investigation, asking about the unpowered Ixomen Sphere with Sebastian later will have him search the trash can for a charger base they had found before, just to find it empty. He will emphasize a few times that if the player had come earlier, maybe the base would have still been around.