Sheaf-Theoretic Transport and Obstruction for Detecting Scientific Theory Shift in AI Agents
This paper develops a finite sheaf-theoretic framework to detect scientific theory shift in AI agents through transport and obstruction. Contexts are organized into a local-to-global structure with source, overlap, target, and validation charts. Obstruction is measured by residual fit, overlap incompatibility, constraint violation, limiting-relation failure, and representational cost. The framework is evaluated on a transition-card benchmark, showing that direct obstruction ranking can distinguish deformation from extension of a source language.
[2605.14033] Sheaf-Theoretic Transport and Obstruction for Detecting Scientific Theory Shift in AI Agents
[Submitted on 13 May 2026]
Title:Sheaf-Theoretic Transport and Obstruction for Detecting Scientific Theory Shift in AI Agents
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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.
Subjects:
Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
Cite as: arXiv:2605.14033 [cs.AI]
(or arXiv:2605.14033v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2605.14033
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: David Olivieri [view email] [v1] Wed, 13 May 2026 18:46:17 UTC (1,371 KB)
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