lean artifact · pending
Artifact ↗Source authenticated
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 , hence , 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 , and that weaker bound is what the release's Lean formalization proves.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 24, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Zauner's conjecture: at most three mutually unbiased bases in dimension six · Mutually unbiased bases in dimension six
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
The Matolcsi-Ruzsa-Weiner Fourier-vanishing conjecture for complex Hadamard matrices of order six evidence for this event
This event attributed to Unreleased internal OpenAI model
VibeMathed record: Zauner's conjecture: at most three mutually unbiased bases in dimension six evidence for this event
Zauner's conjecture: at most three mutually unbiased bases in dimension six parent of this event
Theorem 1.1 (computer-assisted): there are no four pairwise mutually unbiased orthonormal bases in , hence , 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 , and that weaker bound is what the release's Lean formalization proves. parent of this event
Related in family: The maximum number of mutually unbiased bases in dimension six evidence for this event
Lean scope note for this family (lean/docs/266.md) evidence for this event
Lean proof (OAI.MUB6.fourier_and_family_bound) evidence for this event
Act on this frontier