Hypergeometric monodromy and reflection groups

Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions

Elena Fuchs, Chen Meiri and Peter Sarnak

52 pages27 claims indexed23 referencesManuscript 2013-08-12

Coverage, costs and accepted reports

All 49 attempts are terminal. No new paid inference was used for the publication or subsequent exact audits. Counts measure accepted delivery, not mathematical correctness. Native packet assessments precede the later source adjudication; their allegations are not automatically adopted.

Stage Model / effort Accepted / attempted Accounted USD
arbitration gpt-6-astra / max 0/1 1.4780825
arbitration gemini-4-argon / high 1/2 0.6996700
initial-packet gpt-6.1-sol / high 34/34 1.7820600
initial-packet gemini-4-argon / high 2/4 1.0470860
initial-packet claude-fable-5-1 / max 2/4 5.1572000
initial-packet claude-opus-5-5 / max 1/4 2.0897800

Total: $12.2538785 / $25 authorized. Usage/accounting includes failed attempts and is not invoice reconciliation. Native attempt ledger.

Accepted structured mathematical reports

The initial 46 calls included 34 Sol claim/narrative packets and four broader packets for each other provider. Each reviewer saw its assigned frozen arXiv v2 source; none of this constitutes 46 full-paper audits. The accepted arbiter uses preprint numbering; the classification is Theorem 2.6 in JEMS. The two other native arbitration deliveries remain rejected.

Remaining obligations

Other Theorem 4.7 families and the appendix lack completed source adjudication in this dossier. The dimension-five subgroup index is open. The classical Beukers–Heckman and Nikulin theorem statements and application conditions were inspected, but their proofs are accepted as external inputs rather than re-audited. Direct download of the original Nikulin PDF timed out; its primary-article extraction is cached. There is no global green verdict.

The neutral map indexes 27 claims and 23 bibliography references. Selected proof-input edges do not make that map complete. Terminal nodes are sinks only in the recorded graph. Initial opinions, supported local mechanisms, refuted statements and unresolved descendants retain separate origins.

Source record

Additional supporting archive items are identified in the original report. View the manuscript hashes and repository snapshot.