Generative AI is changing a basic premise of educationalassessment: that submitted work can reliably evidence thehuman capacities a credential claims to certify. The chal-lenge is not simply whether students use AI, but what re-mains inferable about learning when some cognitive workhas been delegated to a system. This paper developscogni-tive stewardship, a framework for AI-mediated assessmentthat links the learning claim, delegation boundary, evidencestandard, and safeguards. We then audit verified public gen-erative AI assessment guidance from 30 universities.