# Sheaf-Theoretic Transport and Obstruction for Detecting Scientific Theory Shift in AI Agents

arXiv: https://arxiv.org/abs/2605.14033 · HTML: https://mlsanity.com/paper/2605.14033/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 12 of 12)

- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [ScienceWorld: Is your Agent Smarter than a 5th Grader?](https://mlsanity.com/paper/2203.07540/) (2022)
- [ScienceAgentBench: Toward Rigorous Assessment of Language Agents for Data-Driven Scientific Discovery](https://mlsanity.com/paper/2410.05080/) (2024)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [DiscoveryBench: Towards Data-Driven Discovery with Large Language Models](https://mlsanity.com/paper/2407.01725/) (2024)
- [DISCOVERYWORLD: A Virtual Environment for Developing and Evaluating Automated Scientific Discovery Agents](https://mlsanity.com/paper/2406.06769/) (2024)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding](https://mlsanity.com/paper/2110.03789/) (2021)
- [Sheaf theory: from deep geometry to deep learning](https://mlsanity.com/paper/2502.15476/) (2025)
- [A Sheaf-Theoretic Characterization of Tasks in Distributed Systems](https://mlsanity.com/paper/2503.02556/) (2025)

## Built on by (most cited first, 2 of 2)

- [Capability Sheaves for Compositional Agent-Harness Repair: Controlled Quotients and a Real-Repository Stress Test](https://mlsanity.com/paper/2608.13228/) (2026)
- [Toward Auto-Research: Mining Falsifiable Research Ideas from Paper Knowledge Graphs with Categorical Structure](https://mlsanity.com/paper/2608.20361/) (2026)

## Abstract (arXiv)

Scientific theory shift in AI agents requires more than fitting equations to data. An artificial scientific agent must detect whether an existing representational framework remains transportable into a new regime, or whether its language has become locally-to-globally obstructed and must be extended. This paper develops a finite sheaf-theoretic framework for detecting theory-shift candidates through transport and obstruction. Contexts are organized as a local-to-global structure in which source, overlap, target, and validation charts are fitted, restricted, and tested for gluing. Obstruction measures failure of coherence through residual fit, overlap incompatibility, constraint violation, limiting-relation failure, and representational cost. We evaluate the framework on a controlled transition-card benchmark designed to separate deformation within a source language from extension of that language. The main result is direct obstruction ranking: the intended deformation or extension is usually the lowest-obstruction candidate, and transition type is separated in the benchmark. A constellation kernel over the same signatures is included only as a secondary representational-similarity probe. The aim is not to reconstruct historical paradigm shifts or solve open-ended autonomous theory invention, but to isolate a finite diagnostic subproblem for AI agents: detecting when representational transport fails and extension becomes the coherent next move.