We've made a breakthrough in self-evolving AI scientists moving from "search" to "principled discovery": Scientific discovery requires that the search space itself changes, and an AI scientist must perceive this shift without intervention. We built an AI that achieves this for the first time with the ability to discover the scientific vocabulary it reasons in. Evidence, tools, artifacts, verifiers, failures & claims become typed provenance. We show three distinct modalities: 1) retrieval, adding known objects; 2) search, exploring a fixed schema; and critically: 3) discovery, a verified regime transition. We solve the open-endedness evaluation problem by lifting agentic workflows into a typed copresheaf and proving, via a Kan obstruction, that true discovery is not unbounded generation but a verifiable schema expansion: old evidence is transported by Left Kan extension, and genuine novelty is mathematically quantified by the pointwise residual beyond the transported image - separating discovery from mere search and making novelty objective and measurable rather than a subjective judgment or benchmark delta. Our AI scientist is built in a way that does not pre-conceive the approach it chooses; instead, we endow the system with formal power to adapt, evolve, and reason from first principles. Case studies include: 1⃣Builder/Breaker model that discovers mode-conditioned compliance in proteins; 2⃣CategoryScienceClaw that finds anisotropic fiber-network stiffness rules. Great work in collaboration with my graduate student @fwang108_ @MITdeptofBE F.Y. Wang & M.J. Buehler, Self-Revising Discovery Systems for Science: A Categorical Framework for Agentic Artificial Intelligence, arXiv:2606.01444, 2026 Video