Arithmeticity of Degree-Six Symplectic Hypergeometric Monodromy Groups
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.
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI-discovered
- Method
- Computation
- Field
- Group theory
- Posed by
- Jitendra Bajpai, Martin Dona, Martin Nitsche
- Year posed
- 2025
- Years open
- 1y
- Solved
- 2026-05-25
- Model
- AlphaEvolve
- Vendor
- Google DeepMind
- Collaborators
- J. Maxwell Riestenberg, Diaaeldin Taha, Steve Trettel
- Verification
- Site-confirmed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
two of the three remaining cases; one is still unclassified
What the AI did
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.
Verification
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 arXiv preprint, not peer-reviewed.