Determine the sign u_p in U_p(0) for orders b = 3,4,5

Determine whether, for Calabi–Yau type differential operators of orders b = 3, 4, 5, the sign u_p in the constant Frobenius matrix U_p(0) can be consistently taken to be +1 for all primes p.

Background

The constant matrix U_p(0) encodes the Frobenius action at the MUM point and includes a factor u_p ∈ {±1} along with coefficients α_i constrained by a symplectic condition.

For operators of small orders (b = 3,4,5), prior works provide conjectural expressions for the α_i. The authors highlight an additional conjecture that the sign u_p equals 1 for every prime, which, if true, simplifies the normalization of U_p(0) across all p.

References

Conjectural expressions for the remaining independent constants α_i have been given in refs. for differentials operators with b=3,4,5, for which it is also conjectured that u_p=1 for all p.

— 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 Section 2.2 (following equation (2.17))