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    It is not the case that Gleason's theorem derives the Born rule from frame functions defined on the full Hilbert space lattice, not from value assignments to commuting sets.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Gleason's theorem assumes non-contextual frame functions exist; deriving Born rule from this assumption risks circular reasoning about what needs proving.
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    • 2.The theorem's reliance on separability and dimensionality constraints makes it inapplicable to infinite-dimensional systems common in quantum field theory.
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    • 3.Gleason provides existence results but doesn't explain why nature implements these particular probability measures over other mathematically possible alternatives.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Gleason's theorem directly addresses the full projection lattice structure, avoiding artificial restrictions to commuting observables that limit physical applicability.
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    • 2.Frame functions capture global constraints on probability assignments across the entire Hilbert space, naturally explaining contextuality without ad-hoc assumptions.
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    • 3.This approach derives Born rule necessity from geometric properties of quantum logic itself, not from classical intuitions about simultaneous value assignments.
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