Capability Sheaves for Compositional Agent-Harness Repair

A recent paper on arXiv (2608.13228v1) presents a mathematical approach aimed at addressing failures in AI agent harnesses, which integrate retrieval, routing, state, provenance, and verification. The researchers utilize a finite 'capability sheaf' to model these failures, where stalks represent typed behavior signatures, restriction maps preserve shared fields, and accepted runs serve as valuable global sections. Acceptance is defined by a precise finite constraint-satisfaction problem (CSP), while a linearized relative cohomology class offers diagnostic and search capabilities. In a controlled study involving 20 task clusters, the method incorporates hidden interior mediators with raw states acting as nuisance variables. By quotienting their coboundaries, the candidate budget is cut from 2,000 to 1,000 per cluster, and aligning the hidden state eliminates the gap. The exact CSP aligns with the quotient, indicating invariance to outdated representatives. The method has also been evaluated using a discovery split from the SWE-bench M benchmark. The full paper can be accessed at https://arxiv.org/abs/2608.13228.