Title: A Categorical Framework for Agentic AI in Self-Revising Scientific Discovery

Abstract: The process of scientific discovery extends beyond merely generating answers; it involves fundamentally revising the representational frameworks that define how evidence, artifacts, operations, and verification methods are categorized. This paper presents a category-theoretic model for agentic discovery, specifically applied to materials science. Within a fixed regime $b$ characterized by a schema category $S_b$, the system’s state is modeled as a copresheaf $I_t: S_b \to Set$, with its provenance represented by the category of elements $\int_{S_b} I_t$. Operations within a fixed regime update these states, functioning as endofunctors only when specific refinements that preserve provenance are identified and maintained. In contrast, discovery is defined as a verified transition between regimes, $u: S_b \to S_b'$. During this transition, legacy artifacts are retained and transported via the left Kan extension $Lan_u I_t$. The post-transition state is then compared against this transported content to pinpoint residual information that cannot be explained by functorial transport alone. This approach effectively distinguishes between retrieval, search, and discovery, eliminating the need for subjective notions of novelty. We demonstrate the utility of this framework through two case studies. First, in the Builder/Breaker system, a world model for protein mechanics is updated using a Minimum Description Length criterion; the resulting accepted principle characterizes within-chain flexibility as all-mode elastic compliance, contingent upon participation in slow collective modes—referred to as mode-conditioned compliance. Second, CategoryScienceClaw integrates typed skills, artifacts, open requirements, workflow mutations, gates, stress tests, and public discourse into a proof-bearing graph for knowledge computation. In an analysis of fiber networks, this system documented candidate models, discarded alternatives, AIC gate evaluations, and perturbation tests, ultimately accepting an orientation-tensor anisotropic stiffness surrogate as a superior approximation to an isotropic fiber-count descriptor. Collectively, these examples illustrate how category theory serves dual roles: as a mathematical language for articulating discovery and as an engineering specification for constructing AI systems capable of self-revision.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC