Identify K from the basis change with the K in U_p(0)

Show that, for fourth-order Calabi–Yau type differential operators, the rational number K appearing in the generalized change-of-basis ρ equals the coefficient K occurring in the Frobenius matrix U_p(0).

Background

The constant K appears in two a priori different places: (i) in the generalized basis change ρ that encodes the rational structure, and (ii) in the conjectural formula α_3 = K ζ_p(3) governing U_p(0).

Identifying these two constants would unify the geometric rational-structure input with the arithmetic normalization of Frobenius at the MUM point, providing a coherent framework for the constants that appear in the deformation method.

References

Further, we conjecture that the rational number K appearing in this relation is equal to the coefficient K in the matrix U_p(0). We are not aware of counterexamples to this conjecture.

— Solutions of Calabi-Yau Differential Operators as Truncated p-adic Series and Efficient Computation of Zeta Functions  (2604.01191 - Kuusela et al., 1 Apr 2026) in Appendix B