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quantum mechanics fulfils the conditions: A mathematical model about a sufficiently large set of natural phenomena and it cannot be further reduced to more fundamental concepts, atleast not yet. The same holds for classical mechanics, but only for low velocities, when the velocity is high, approaching the speed of light, then the theory of (special) relativity is needed. classical electromagnetism also is a mathematical model about a sufficiently large set of natural phenomena where the first principle I think are the Maxwell equations. That is however a field theory and I do think that this theory is correct in extreme situation (high Energy or very small scales).
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