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.