The Kochen-Specker theorem demonstrates that any hidden-variable theory reproducing QM statistics must be contextual, making FUNC's applicability to non-commuting observables formally inconsistent.

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Contextual/Contextuality(the key constraint the theorem imposes): The idea that a property's value depends on what other properties you're measuring at the same time—like saying an answer changes based on the question you ask alongside it.
FUNC(as used in physics philosophy): An abbreviation for a specific theory in quantum mechanics (the study of how tiny particles behave); without more context, this refers to a particular interpretation or model of how quantum physics works.
Formally inconsistent(describing the relationship between FUNC and the theorem's conclusions): Logically contradictory or self-contradictory according to mathematical rules—like trying to prove something is both true and false at the same time.
Hidden-variable theory(a type of explanation for quantum mechanics): The idea that quantum particles have real, definite properties we just can't see or measure directly—like saying a coin is secretly heads or tails even before you flip it.

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