Generative AI is changing a basic premise of educational assessment: that submitted work can reliably evidence the human capacities a credential claims to certify. The challenge is not simply whether students use AI, but what remains inferable about learning when some cognitive work has been delegated to a system. This paper develops cognitive stewardship, a framework for AI-mediated assessment that links the learning claim, delegation boundary, evidence standard, and safeguards. We then audit verified public generative AI assessment guidance from 30 universities. Using a pre-specified scoring codebook--a written, source-grounded rubric--four open-weight LLM models applied the rubric as structured coders, with scores averaged to reduce dependence on any single model's bias. The audit shows that public policies are becoming better at classifying AI use than at explaining what evidence and protections preserve credential validity. Boundaries are more visible than evidence standards; safeguards are uneven; and guidance is clearest when AI use resembles final-output substitution rather than feedback, access, verification, or professional workflow. The takeaway is that permission categories are necessary but insufficient. Universities need policies that make the certification logic visible: what learners may delegate, what they must still demonstrate, and how institutions will protect fair evidence rather than merely monitor AI use.

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