Show the generalized change-of-basis yields the rational structure in order 4

Establish that the generalized change-of-basis matrix ρ described in Appendix B produces a basis with rational monodromy for every fourth-order Calabi–Yau type differential operator that admits a rational structure.

Background

Appendix B discusses a generalized Γ-class-inspired change of basis ρ relating the Frobenius periods to a period vector with rational monodromy, parameterized by rational data including a number K.

The authors posit that this ρ suffices to capture the rational structure for all fourth-order Calabi–Yau type operators that possess such a structure, extending beyond the standard Γ-class formula and known geometric examples.