Strong jump traceability versus LR-reducibility

Determine whether strong jump traceability reducibility $\leq_{SJT}$ implies LR-reducibility $\leq_{LR}$.

Background

The two reducibilities compare oracle strength through traceability and preservation of Martin-Löf randomness. The implication is known when the right-hand side is the empty set, but is unresolved in general.

References

Does $\leq_{SJT}$ imply $\leq_{LR}$?

— Open Problems in Mathematical Logic  (2608.26628 - Barmpalias et al., 27 Aug 2026) in Section 2, subsection Computability Theory