A Sharp Local-Question Threshold for GHZ-Equatorial Completeness in Four-Player XOR Games
Published in arXiv preprint, 2026
This work identifies the exact point at which a perfect four-player binary XOR game is no longer guaranteed to have a GHZ-equatorial realization. It proves that three or fewer active questions per player always suffice, then gives an explicit eight-clause counterexample with four questions per player. The arguments combine integral incidence obstructions, ordered noncommutative refutations, combinatorial matching techniques, and Magnus-coefficient analysis.