CategoryScienceClaw

Self-revising discovery framework that adds a category-theoretic, proof-carrying layer to the ScienceClaw agentic execution substrate so that regime transitions — schema changes admitting new evidence types — can be machine-verified and audited.

   
Affiliation MIT — Laboratory for Atomistic and Molecular Mechanics (Buehler group)
First introduced 2026-05 (arXiv preprint)
Lifecycle stages Multi-stage (hypothesis generation, simulation-based experiment design, analysis, with verified regime transitions)
Autonomy level Semi-autonomous (typed skills, immutable artifacts, open needs, workflow mutation, gates, stress tests, and public discourse coordinated as a typed knowledge–computation graph)
Domain focus Materials science / mechanics (protein-mechanics, fiber-network mechanics)
Availability Open source

Approach

The paper develops a category-theoretic account of agentic scientific discovery. In a fixed regime, the system state is a copresheaf Iₜ : Sb → Set and provenance is the category of elements; fixed-regime operation is an endofunctorial update on such states. Discovery is instead a verified regime transition u : Sb → Sb' — old artifacts are preserved, transported by left Kan extension Lan_u Iₜ, and compared with the post-transition state to identify residual content beyond functorial transport. This distinguishes retrieval, search, and discovery without subjective novelty.

Two instantiations are presented. Builder/Breaker revises a protein-mechanics symbolic world model under a Minimum Description Length gate; the accepted law expresses within-chain flexibility as mode-conditioned compliance (all-mode elastic compliance conditioned by slow collective-mode participation). CategoryScienceClaw wraps the underlying ScienceClaw agentic execution substrate — where typed skills, immutable artifacts, open needs, workflow mutation, and public discourse form a knowledge–computation graph — with a categorical proof-carrying layer.

Validation

A fiber-network mechanics worked example records candidate models, rejected alternatives, an AIC gate, perturbation tests, and an accepted orientation-tensor anisotropic stiffness surrogate that supersedes an isotropic fiber-count descriptor. Model selection itself — including the rejected alternative — is recorded as typed provenance.

The Builder/Breaker case study produces a 54.3-bit MDL gain on accumulated evidence; signed model-code changes confirm the discovery is genuine schema expansion rather than refit.

Notable results

  • First operational categorical account of self-revising AI scientific discovery, separating fixed-regime search from regime-extending discovery via Kan-extension transport.
  • Builder/Breaker delivers a published mode-conditioned compliance law for protein mechanics, accepted under an MDL gate.
  • Worked fiber-network example materializes accepted models, rejected alternatives, gates, stress tests, and regime-transition claims as typed artifacts and morphisms.

Primary paper

Wang & Buehler, “Self-Revising Discovery Systems for Science: A Categorical Framework for Agentic Artificial Intelligence,” arXiv:2606.01444 (May 2026).

Other references

Code