Kanade–Russell mod 9 conjectures

Prove the Kanade–Russell mod 9 partition conjectures, which remain unresolved despite the proof of the corresponding mod 12 conjectures.

Background

The paper situates its search algorithm within the discovery of partition identities, particularly the systematic work of Kanade and Russell. It notes that their mod 12 conjectures have already been proved, whereas the mod 9 conjectures remain unresolved. Because the authors explicitly identify these conjectures as still open, this constitutes an open problem referenced in the paper, although it is not the central problem addressed by the paper.