Determine whether the rigidity classification extends beyond the census

Determine whether a Petersson-rigid lattice outside the 100-root-basis census can have a quaternion discriminant different from 6, 10, or 22.

Background

The census finds exactly three Petersson-rigid lattices, with quaternion discriminants 6, 10, and 22. These are precisely the genus-zero Shimura-curve discriminants appearing in the census.

The rim of the census is explicitly only a one-edit probe rather than a classification, so the paper does not establish that no rigid lattice exists outside the enumerated core and rim.