Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 266-02. Exact Fourier certificates for complex Hadamard matrices of order six
Manuscript map · lines 7775–7784
OpenAI@2026-10-07#rem:oai-p-266-02
Authors: OpenAI. Family 266.
Title: Exact Fourier certificates for complex Hadamard matrices of order six.
Abstract: We prove the Fourier-vanishing conjecture of Matolcsi, Ruzsa, and Weiner: every complex Hadamard matrix of order six outside Tao's cubic equivalence class has a vanishing character sum at every permutation of $(1,1,1,-1,-1,-1)$. We also give an exact certificate excluding seven mutually unbiased bases in ℂ6; by Weiner's completion theorem, this yields an upper bound of five. Both certificates use only integer and rational arithmetic, and the complete verifier is included.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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