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

TL;DR

This paper introduces a sheaf-theoretic framework to detect when AI agents' scientific theories can be transported or need extension, using obstruction measures to identify theory shifts.

Contribution

It develops a finite sheaf-theoretic method for diagnosing theory transport failures and extensions in AI agents, with a benchmark evaluation.

Findings

Intended deformations or extensions usually have the lowest obstruction scores.

The framework effectively separates deformation within a language from its extension.

Obstruction ranking can identify the most plausible theory shift candidate.

Abstract

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.