Math RefereeHyperbolic monodromy groups for the hypergeometric equation and Cartan involutions
Elena Fuchs, Chen Meiri and Peter Sarnak
The proposed argument
Use companion matrices to encode integral hypergeometric monodromy. Classify almost-interlacing cyclotomic parameters and construct invariant quadratic lattices. Compare Cartan involutions along edges of a minimal-distance graph with a hyperbolic reflection subgroup. Combine its quotient with Vinberg/Nikulin nonreflectivity criteria to certify thinness for stated families. Tabulate low-dimensional examples and separately examine dimension-three arithmetic cases in an appendix.
Initial model packets used arXiv v2 (52 pages, 12 August 2013). Relevant statements and applications were separately checked against the 55-page JEMS 16 (2014), 1617–1671 edition. External proof-input cutoff: received 11 August 2013. The source editions and their theorem numbering are kept distinct.
Reading order
Follow the dependencies
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Your independent assessment
Separate classification hypotheses from thinness criteria; identify the actual integral lattice, finite-order generator and reflection quotient at each application.