Resolving Thinness of Degree-Six Symplectic Hypergeometric Monodromy Groups

@misc{riestenberg2026resolving,
  title = {{Resolving Thinness of Degree-Six Symplectic Hypergeometric Monodromy Groups}},
  author = {J. Maxwell Riestenberg and Diaaeldin Taha and Steve Trettel and Anna Wienhard},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.25935},
  eprint = {2605.25935},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.25935},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Resolving Thinness of Degree-Six Symplectic Hypergeometric Monodromy Groups
AU  - J. Maxwell Riestenberg
AU  - Diaaeldin Taha
AU  - Steve Trettel
AU  - Anna Wienhard
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2605.25935
UR  - https://arxiv.org/abs/2605.25935
AB  - We prove arithmeticity for two degree-six symplectic hypergeometric monodromy groups and thinness for a third case. These are the three open cases called C-32, C-47, and C-55 in the paper [BDN25] by Bajpai--Dona--Nitsche. This hence settles thinness of primitive integral symplectic hypergeometric monodromy groups of degree-six, according to the tabulation by Bajpai--Dona--Singh--Singh [BDSS21]. The arithmeticity certificates were found with AlphaEvolve and the thinness certificate is a ping pong table found by a harness that was configured to run ChatGPT 5.5. These certificates are then independently verified with exact matrix arithmetic over Q using a computer. We also include illustrations of limit sets of several degree-six symplectic hypergeometric monodromy groups.
ER  -