Identification of unresolved Apéry-like limits

Identify the exact values of the unresolved Apéry-like limits \(L=\lim_{n\to\infty} b_n/a_n\) associated with the two platonic sequences denoted \((2)\) and \((2)\) in the paper’s discussion and marked by question marks in the accompanying table.

Background

For each relevant Picard–Fuchs recursion, the paper considers a second solution and the limiting ratio of its coefficients to those of the holomorphic-period solution. Several limits are identified as logarithmic expressions, but some are known only numerically. The authors explicitly report that they were unable to identify the constants for two of the listed sequences.

References

In some cases, the number was identified and turns out to be a logarithmic term. In other cases, for example for $(2)$ and $(2)$, the limit was computed to high precision, but we, nor {\tt ChatGPT} or {\tt Claude}, were not able to identify the constant up to now.

— The platonic elliptic surfaces  (2608.25644 - Gegelia et al., 26 Aug 2026) in Section 8, subsection “Apéry-like limits”