Finite-dimensional quantum mechanics, including the Born rule and complex Hilbert space structure, follows uniquely from distinguishability plus finite capacity and self-referential consistency.
Acz´ el,Lectures on Functional Equations and Their Ap- plications(Academic Press, 1966)
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Existence as Distinguishability: Quantum Mechanics from Finite Graded Equality
Finite-dimensional quantum mechanics, including the Born rule and complex Hilbert space structure, follows uniquely from distinguishability plus finite capacity and self-referential consistency.