Remark: Family 266. Exactly three mutually unbiased bases in dimension six

Proves $N(6)=3$, resolving Zauner s dimension-six mutually unbiased bases conjecture: three such bases exist in ${\mathbb{C}}^6$, but four cannot. The exclusion is a complete certified computation under the stated binary64 arithmetic and compiler conditions. An independent companion proves the Matolcsi–Ruzsa–Weiner Fourier-vanishing conjecture for order-six complex Hadamard matrices outside Tao s cubic equivalence class.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.