Remark: Family 179. The circulant Hadamard conjecture

Proves that real circulant Hadamard matrices exist exactly in orders $1$ and $4$, resolving the circulant Hadamard conjecture. Together with classical Barker-sequence results, this shows that binary sequences whose nontrivial aperiodic autocorrelations have magnitude at most $1$ exist at lengths $n>1$ exactly when $n\in \{2,3,4,5,7,11,13\}$.

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.