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The Laws of The Multiverse™
Scientists will show you a thousand different complex charts of how different dimensions' energies overlap to different effects, rant to you for hours about how some dimensions have different laws of physics, would you stop calling it magic -- and yeah, they're right. But for all intents and purposes: fuck it, it's magic. I don't want to say "science that we can't comprehend with our puny non-scientist minds" every time. That'd get old fast.
People don't just have magic naturally; they have to come by it somehow. The root of pretty much all magic is eldritch powers that people either purposely make pacts with or accidentally walk into (guess which option is more common). These deals can range from becoming super powerful but being completely hapless to the whims of whatever you got yourself into to getting employed at a grim reaping agency. In general, the more powerful someone is, the tighter they're bound to their power and the less free will they have. Some poor souls get in so deep they're little more than meat suits being puppeted about.
Basically, if someone has magic, they're a warlock.
Cosmology
There are lots and lots of religions and cults out there with different beliefs as to the answer to that. The majority of people belive in the Big Bang, but it's not the dominant belief by much.
No one really knows and I'm sure as hell not going to pretend I do just because I created the thing. However, I can tell you that the multiverse rests in the mouth of a very large snake. If you know and are willing to divulge any information regarding how this snake got there or the color of the snake, I would be much obliged.
Principal Geography & Features
This is tricky because there are tons of dimesions that all look vastly different and in fact may follow completely different rules of physics. Earth's geography? Exactly the same as our Earth's. Other dimensions vary hugely in geography, from the abandoned playgrounds that were built by no one and are considered geological structures in the Umbrella to the infinite rolling fields of the Void where the dead are buried.
Initial Active Setting
The story will start mostly on Earth and a few dimensions a little sideways to it, but throughout the story our protagonists will end up hopping all over the multiverse. There is no real order to dimensions and it's exceedingly difficult to figure out how close certain dimensions are to certain others, and it doesn't make much of a difference when traveling them anyway! So I can't put a clear active setting on it.