2026/05/31 by Fiona Y. Wang, Markus J. Buehler · 2 voices
Computer Science · Physics and Astronomy · Mathematics · #cs.AI #cond-mat.mtrl-sci #cs.CL #cs.LG #math.CT
Scientific discovery is not only answer generation but revision of the representational regime in which evidence, artifacts, operations, and verifiers are typed. We develop a category-theoretic account of agentic discovery for materials science. In a fixed regime b with schema category Sb, the system state is a copresheaf It: Sb -> Set, and provenance is the category of elements ∫Sb It. Fixed-regime operation is an update on such states, endofunctorial only when provenance-preserving refinements are specified and preserved. Discovery is instead a verified regime transition u: Sb -> Sb': old artifacts are preserved, transported by the left Kan extension Lanu It, and compared with the post-transition state to identify residual content beyond functorial transport. This separates retrieval, search, and discovery without subjective novelty. We instantiate the framework in two systems. In Builder/Breaker, a protein-mechanics world model is revised under a Minimum Description Length gate; the accepted law expresses within-chain flexibility as all-mode elastic compliance conditioned by slow collective-mode participation, or mode-conditioned compliance. In CategoryScienceClaw, typed skills, artifacts, open needs, workflow mutation, gates, stress tests, and public discourse become a proof-carrying knowledge-computation graph. A fiber-network example records candidate models, rejected alternatives, an AIC gate, perturbation tests, and an accepted orientation-tensor anisotropic stiffness surrogate over an isotropic fiber-count descriptor. Together, the cases show how category theory can be both a mathematical language for discovery and an engineering specification for self-revising AI discovery systems.