Converse Weihrauch reductions for dashed-arrow comparisons

Determine whether the converse Weihrauch reduction holds for each pair of Laver-partition principles and benchmark degrees connected by a dashed arrow in Figure 1, that is, whether the displayed reduction A ≤W B can be reversed as B ≤W A.

Background

The paper presents a diagram of the arithmetical Weihrauch degrees associated with the open and clopen Laver partition theorems, together with related choice, closed choice, and transfinite-comprehension principles. Solid arrows denote strict Weihrauch reductions, whereas dashed arrows record only a known reduction in one direction.

The authors explicitly state that, for a dashed arrow from A to B, they do not know whether the reverse reduction holds. Thus the unresolved issue concerns the exact Weihrauch relationships represented by the dashed comparisons in the diagram, including whether any of those one-way reductions are actually equivalences.

References

We draw a dashed arrow from $A$ to $B$ to indicate that $A \leq_{W} B$ (but we do not know whether $B \leq_{W}A$).

— Computable aspects of the Laver partition theorem  (2608.24716 - Marcone et al., 25 Aug 2026) in Figure 1, caption summarizing the relative positions of the arithmetical Weihrauch degrees