No reduction from NP to cPIR

A reduction of class unstated from NP to cPIR would imply a contradiction.

Statement

Migrated verbatim from single-server-private-information-retrieval § Other results:

• Single-round PIR cannot be based on NP-hardness unless PH collapses to the second level — LV15

Notes

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• Barrier Q is a complexity claim (‘PH collapses to the second level’) — fits the barrier schema exactly; hypothesis is ‘NP-hardness of the underlying problem’, typed here as the class NP.
• The reduction class is not named on the page (LV15 concerns general/black-box reductions from an NP-hard problem); ‘black-box’ is my inference, not the page’s word.