Phangara's conjecture: every order-six S-Hadamard matrix is equivalent to Tao's cubic matrix
Proposition 3.1: if and its entrywise square are both complex Hadamard matrices of order six, then is equivalent to Tao's cubic matrix; in particular all its dephased entries are cube roots of unity. The manuscript notes that uniqueness of the cube-root class was already known from Butson classifications (Lampio-Ostergard-Szollosi; Liang-Chen-Long-Qiu); the new step derives cube-root entries from the two Hadamard conditions for arbitrary phases. It says nothing about other orders.
Exact FrontierDelta
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: Phangara's conjecture: every order-six S-Hadamard matrix is equivalent to Tao's cubic matrix · Order-six S-Hadamard classification
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
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
Proposition 3.1: if and its entrywise square are both complex Hadamard matrices of order six, then is equivalent to Tao's cubic matrix; in particular all its dephased entries are cube roots of unity. The manuscript notes that uniqueness of the cube-root class was already known from Butson classifications (Lampio-Ostergard-Szollosi; Liang-Chen-Long-Qiu); the new step derives cube-root entries from the two Hadamard conditions for arbitrary phases. It says nothing about other orders. parent of this event
Phangara's conjecture: every order-six S-Hadamard matrix is equivalent to Tao's cubic matrix parent of this event
VibeMathed record: Phangara's conjecture: every order-six S-Hadamard matrix is equivalent to Tao's cubic matrix evidence for this event
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