🤖 AI Summary
This work addresses the challenge of determining whether a scientific theory can be transferred to a new context or requires an extension of its representational language. It proposes a diagnostic framework grounded in finite sheaf theory, formalizing “obstructions” as computable metrics—such as residual fitting error, overlap incompatibility, and constraint violation—through the local–global structure of source, overlap, target, and validation diagrams. The approach introduces constellation kernels as probes for representational similarity and, for the first time, translates the sheaf-theoretic notion of obstruction into an actionable diagnostic tool for AI-based scientific agents. This enables clear discrimination between internal deformations of a theory and cases necessitating genuine language expansion. Evaluated on the transition-card benchmark, the method accurately ranks transfer obstructions, identifies minimal-obstruction candidates, and cleanly separates the two types of theoretical change.
📝 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.