In the universe of Paranoia Agent, Ayumu never entered the plot of Azumanga Daioh. And thus instead of growing up to be Osaka and having some very close friends, she became very lonely and changed her name to Tsukiko Sagi (as sort of a pseudonym for her design career).
Chiyo-chichi was able to appear to both Sakaki and Osaka without ever mentioning him to each other because Osaka has reality warping capabilities that are very weak. In Paranoia Agent, her reality warping powers are so strong that she makes Maromi come to life and makes Shounen Bat a physical entity.
That's why Tsukiko Sagi looks so disturbingly similar to Osaka and the reason why Osaka is such a Nightmare Fuel Station Attendant.
- "Magical" superpowers? Failed to find friends? Associated with the moon and with bad dreams? Surrounded by Ridiculously Cute Critters? That just screams Nightmare Moon.
- Seems I wasn't the only one with this idea. Many parallels between this show and Persona can be made, especially to P2.
- Hell, much more than that - they also both are enigmatic figures that either stand menacingly or attack, have Offscreen Teleportation, really the early Slender Man stuff in general is reminiscent of Paranoia Agent.
- Maromi represents innocence ("I didn't know!") and Little Slugger represents transfer of blame ("Someone else did it/My hands were tied.")
- To be fair the show pretty much states this outright. Although it's unclear to the viewer in the first episode whether or not Sagi is schizophrenic, she believes Maromi to still be with her. It's Maromi who brings up Shounen Bat after the initial "attack" as a way for Sagi to escape the responsibility for breaking her own ankle to escape the pressures at work, the same way she escaped the responsibility for what really happened to her pet. Maromi and Shounen Bat are evenly matched in size and power in the last episode until Maniwa states that Sagi is responsibile for her dog's death, at which point they merge, so on some level they're both the same defense mechanism for Sagi and therefore likely the same being.
- This also adds an alternate reading to Maromi's final lines, telling Sagi to run. He may not be telling her to escape from the Advancing Wall of Doom, but to keep rejecting the truth and "run away" from her problems.