Zauner's conjecture: at most three mutually unbiased bases in dimension six

Theorem 1.1 (computer-assisted): there are no four pairwise mutually unbiased orthonormal bases in $\mathbb C^6$, hence $N(6)=3$, the lower bound coming from the explicit tensor-product triple. The proof covers every second basis (an arbitrary complex Hadamard matrix) by certified phase balls and excludes two further bases in each by a clique search with rounding margins. It is conditional on the stated binary64 arithmetic and on the complete execution it documents. The companion paper gives an exact rational certificate only for $N(6)\le5$, and that weaker bound is what the release's Lean formalization proves.

Theorem 1.1 (computer-assisted): there are no four pairwise mutually unbiased orthonormal bases in $\mathbb C^6$, hence $N(6)=3$, the lower bound coming from the explicit tensor-product triple. The proof covers every second basis (an arbitrary complex Hadamard matrix) by certified phase balls and excludes two further bases in each by a clique search with rounding margins. It is conditional on the stated binary64 arithmetic and on the complete execution it documents. The companion paper gives an exact rational certificate only for $N(6)\le5$, and that weaker bound is what the release's Lean formalization proves.