Distinguish arithmetic and geometric Johnson images for closed surfaces

Develop effective methods for distinguishing the arithmetic Johnson image from the original geometric Johnson image at the level of the mapping class group of a closed surface.

Background

The paper notes that several obstructions detect Galois obstructions for the mapping class group of a surface with boundary, but that no obstruction is currently known to detect any Galois obstruction in the Johnson cokernel for a closed surface. This motivates the unresolved question of whether the arithmetic and geometric Johnson images can be effectively separated in the closed-surface setting.

References

Are there effective methods for distinguishing the arithmetic Johnson image from the original geometric Johnson image at the level of the mapping class group of a closed surface?

— The first Galois obstruction in the Johnson cokernel  (2608.17673 - Morita et al., 18 Aug 2026) in Section 7, Section “Questions,” third Question environment