Conjectured lower bound for the total forward-only decision problem

Prove the conjectured lower bound for the total decision problem studied by Holman, Ramachandran, and Yirka in the forward-only in-place oracle model.

Background

The paper compares its existential bounded-error decision separation with the forward-only in-place results of Holman, Ramachandran, and Yirka. It explicitly distinguishes the promise problem established here from the different total decision problem studied in that prior work.

The authors state that their construction does not establish the conjectured lower bound for that total problem. Thus, proving the conjectured lower bound remains outside the results of the paper and is identified as an unresolved problem.

References

The in-place model studied by Holman, Ramachandran, and Yirka is also forward-only. Their work establishes separations for simulation and coherent state conversion and poses a different decision problem. The promise problem here proves an existential bounded-error decision separation; it does not prove the conjectured lower bound for their particular total problem.

— Random Garbage Separates XOR from Forward-Only Queries  (2609.03628 - Elbassioni et al., 3 Sep 2026) in Section 5, Discussion