I'll throw my own towel into the theory-crafting game, and with all this talk recently about the gods using the human characters as hosts and some of the characters potentially being gods, I'll suggest that Maya is the god of strays. Her inability to remember anything about her life before meeting Akira may be an aspect of her godhood, and all the references to stray cats connected with her might just be metaphorical. As far as Sekai's disdain for Maya, it may be due to Maya having a completely different dynamic with Akira than any other character (potentially as an aspect of her godhood). We can see that Akira viewed Maya more as an equal than any of the other characters (both from his predatory advances towards her being turned on their head so early on in the story as well as Maya's long-term experience in the time loop acting as a guide for him). Whether that's because of Maya's personality or her aspect of godhood taking up so much of Akira's attention as part of being "adopted" into his household (literally or figuratively, it's kinda unclear), her dynamic with Akira is almost completely opposite of Sekai's dynamic with Akira and her expected behavior from him. Of course, if all three of these characters are gods (with or without knowing it), that makes this dynamic even more interesting...
Yeah, I think that'll be my pet theory I'll be running with for now.
