Measuring What Persists: Conditioning Mechanisms and a Geometric Framework for AI Agent Identity

The article presents a new geometric framework for assessing AI agent identity using $\sqrt{\mathrm{JSD}}$ metric spaces and magnitude homology from enriched category theory, addressing the issue of identity drift in long-context applications. Key findings include a two-mechanism conditioning structure that identifies clusters related to identity specification and behavioral richness, demonstrating a significant increase in response patterns with the proposed framework. This work is crucial for practitioners as it offers a method to quantitatively measure and potentially mitigate identity drift in AI agents, enhancing their reliability in long-term deployments.