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arXiv · 2605.14033

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

David N. Olivieri·Roque J. Hernández
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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.

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David N. Olivieri, Roque J. Hernández. 2026-05-13. Sheaf-Theoretic Transport and Obstruction for Detecting Scientific Theory Shift in AI Agents. https://arxiv.org/abs/2605.14033

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