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Dark matter is pretty well defined within a particular model, not magic. You can take lambda-CDM, a very simple model, run a simulation, and compare it to observations.

I can't really comment on why MOND is magic. That seems a bit unfair, it's just a phenomenological modification of F=ma, and can similarly be simulated and compared to observations.

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Did the model predict dark matter, or was dark matter introduced to get the model closer to observed reality?

AFAIUI (layman, at best) it's a bit of both. There are multiple independent[1] lines of evidence, some of those led to the formation of the Dark Matter model, others were since discovered and just so happen to also conform to that model.

[1] Maybe that's really the big question here.

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