Separate EFI pairs from inefficiently verifiable one-way puzzles

Establish whether there exists an oracle relative to which EFI pairs exist but one-way puzzles, including the inefficiently verifiable notion, do not, without restricting distinguishers to coherent-last access.

Background

One-way puzzles imply EFI pairs, but the converse is not known. The paper constructs a separation only for a restricted oracle-access model in which all oracle interactions are classical except for one final coherent query. The broader question asks whether the separation can be achieved for an unrestricted oracle model while retaining EFI pairs and eliminating even inefficiently verifiable one-way puzzles.