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Proofs of Bell-Kochen-Specker contextuality demonstrate that there exists sets of projectors that cannot each be assigned either 0 or 1 such that each basis formed from them contains exactly one 1-assigned projector. Instead, at least some of the projectors must have a valuation that depends on the context in which they are measured. This motivates the question of how many of the projectors must have contextual valuations. In this paper, we demonstrate a bound on what fraction of rank-1arXiv:1712.03766v1 fatcat:zdg3iykjunajzmatwpnvucc5lu