Arithmeticity of Degree-Six Symplectic Hypergeometric Monodromy Groups

Precise statement

Bajpai, Dona and Nitsche left three degree-six symplectic hypergeometric monodromy groups unclassified as arithmetic or thin. Two of the three, C-47 and C-55, are arithmetic.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

AlphaEvolve

The arithmeticity certificates were found with AlphaEvolve and then independently verified with exact matrix arithmetic over the rationals, so the search was the model's and the verification was exact rather than trusting.

Provider: Google DeepMind · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

The certificates are exact objects verified by exact rational matrix arithmetic, which is the right kind of check for a search result. arXiv preprint, not peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-05-25

   arXiv:2605.25935 - Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups

   two of the three remaining cases; one is still unclassified

Known method families

computation (source-reported)

Source-reported tools: computation.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.