Determine whether mixed-banknote public-key quantum money survives the oracle

Determine whether public-key quantum money schemes with mixed banknotes survive the counting oracle that eliminates one-way puzzles and classical-output quantum hardness.

Background

The oracle rules out pure-banknote quantum money mini-schemes because such schemes imply one-way puzzles. The cited implication does not cover the mixed-banknote notion, so the oracle's effect on public-key quantum money with mixed banknotes remains unresolved.

References

Whether public-key quantum money with mixed banknotes survives the oracle is open, since the reduction of produces a mini-scheme with a pure banknote and the mixed notion of is not covered (\Cref{sec:no-owpuzz}).

— EFI Pairs Without One-Way Puzzles: Oracle Separations from Communication Complexity  (2609.11901 - Mantri, 10 Sep 2026) in Section 4.2, The scope of these inferences; Section 7, Discussion and open problems