Use First, Verify Later: AI Mathematical Discovery and the Operative Standards of Acceptance

When AI mathematical discovery outpaces human verification, social demand can force time-bound decisions about adoption. The HYC theorem distinguishes two directions: HYC1 identifies operative standards when duty-bound institutions cannot verify or abstain; HYC2 reconstructs such standards from decisions already issued without verification. Historical cases show that use, formal checking, and understanding can occur at different times. AI may also build on unverified results before human checks finish. Where society has no urgent demand, researchers can defer adoption, provided they retain time and an independently auditable record. Information saturation may undermine that capacity.