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

Abstract

AI agents in long-context applications drift from their specified identity. Current methods detect this only after qualitative degradation is visible. We present a geometric framework for measuring identity structure using $\sqrt{\mathrm{JSD}}$ metric spaces and magnitude homology from enriched category theory, where identity is non-geodesic structure and drift is its relaxation toward the geodesic. Validated on a persistent AI agent, the framework's strongest empirical finding is a two-mechanism conditioning structure: cross-condition distances reveal an identity-vacuum cluster where the identity specification fills a behavioral void, and a safety-basin cluster where it displaces from post-training attractors. An equilateral probe baseline confirms that the identity specification creates measurable behavioral richness (55 unique response patterns vs. 1 for the base model) at maximum probe separation. A first-order perturbation theory for equilateral configurations predicts magnitude changes from perimeter changes alone, with shape perturbations first-order cancelled by the $S_n$ symmetry; the formula is self-consistent at the observed perturbation amplitudes. A drift experiment measuring magnitude decrease under context pressure was subsequently found to reflect repetitive-padding artifacts rather than genuine context-length drift; diverse padding produces no measurable deformation through 150K tokens. The magnitude homology framework's full diagnostic promise -- detecting anisotropic contraction and structural collapse via homological simplification -- is architecturally grounded in the perturbation theory and selection rules but remains empirically unconfirmed.