Self-Revising Discovery Systems for Science: A Categorical Framework for Agentic Artificial Intelligence

2026-05-31

AI Summary

Scientific discovery necessitates dynamically revising the representational frameworks that underpin evidence, operations, and validation. This work proposes the first agent-driven framework grounded in category theory, modeling system states as copresheaves and employing left Kan extensions to enable verifiable transitions between representational systems while rigorously distinguishing retrieval, search, and discovery processes. By integrating categorical element integrals, the minimum description length principle, AIC gating, and perturbation testing, the framework formally characterizes representational shifts and knowledge evolution. Applied to protein mechanics and fibrous networks, it successfully derives a pattern-conditioned elastic compliance law and a directional tensor-based anisotropic stiffness surrogate model, fully documenting the trajectory of knowledge evolution throughout the discovery process.

Abstract

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 S_b, the system state is a copresheaf I_t: S_b -> Set, and provenance is the category of elements \int_{S_b} I_t. 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: S_b -> S_b': old artifacts are preserved, transported by the left Kan extension Lan_u I_t, 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.

Problem

• scientific discovery
• representational regime
• agentic AI
• category theory
• self-revising systems

Innovation

• category theory
• agentic AI
• representational regime transition
• left Kan extension
• self-revising discovery