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OpenAI reports: Mutually unbiased bases in dimension six

OpenAI reports that the maximum number of mutually unbiased orthonormal bases in complex dimension six is three, using an exhaustive computer-assisted exclusion of four bases under specified arithmetic and compiler conditions.

Sources for this record

What was already known

Three bases can be constructed in dimension six. An exact maximum requires excluding four arbitrary bases, not only previously studied Hadamard families or numerically sampled candidates.

What changed and why it matters

Matches the known construction with an unrestricted reported upper bound in the stated dimension.

The AI contribution

OpenAI attributes these manuscripts to its internal model. The entry does not infer individual human contributions beyond that publisher attribution.

Limitations

The computer-assisted upper bound depends on the documented complete execution and binary64 arithmetic/compiler contract. AIProofWatch has not rerun that pipeline; this is not a Lean checking claim. Preprint. This is a source-statement and significance assessment, not a proof audit. No independent checking or successful formal compilation is asserted by this entry.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The publisher reports the scoped result. AIProofWatch has not independently validated its correctness.

Accessible artifact / proof

The original written argument is accessible. Availability does not establish a successful proof check or Lean verification.

Correction and publication history

2026-10-11 · publication

Historical report added after statement, scope, and importance review. No proof audit or formal checking asserted; subscriber alerts disabled.

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