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

arXiv: https://arxiv.org/abs/2606.21843 · HTML: https://mlsanity.com/paper/2606.21843/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 31 references that are in the map.
- First posted on arXiv 20 Jun 2026.

## Builds on (most cited first, 20 of 20)

- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Discovering Language Model Behaviors with Model-Written Evaluations](https://mlsanity.com/paper/2212.09251/) (2022)
- [LLMs Get Lost In Multi-Turn Conversation](https://mlsanity.com/paper/2505.06120/) (2025)
- [Persona Vectors: Monitoring and Controlling Character Traits in Language Models](https://mlsanity.com/paper/2507.21509/) (2025)
- [The Assistant Axis: Situating and Stabilizing the Default Persona of Language Models](https://mlsanity.com/paper/2601.10387/) (2026)
- [Get my drift? Catching LLM Task Drift with Activation Deltas](https://mlsanity.com/paper/2406.00799/) (2024)
- [Measuring and Controlling Instruction (In)Stability in Language Model Dialogs](https://mlsanity.com/paper/2402.10962/) (2024)
- [Examining Identity Drift in Conversations of LLM Agents](https://mlsanity.com/paper/2412.00804/) (2024)
- [An enriched category theory of language: from syntax to semantics](https://mlsanity.com/paper/2106.07890/) (2021)
- [Drift No More? Context Equilibria in Multi-Turn LLM Interactions](https://mlsanity.com/paper/2510.07777/) (2025)
- [Metric Space Magnitude for Evaluating the Diversity of Latent Representations](https://mlsanity.com/paper/2311.16054/) (2023)
- [Metric Space Magnitude and Generalisation in Neural Networks](https://mlsanity.com/paper/2305.05611/) (2023)
- [The magnitude of categories of texts enriched by language models](https://mlsanity.com/paper/2501.06662/) (2025)
- [The Shape of Adversarial Influence: Characterizing LLM Latent Spaces with Persistent Homology](https://mlsanity.com/paper/2505.20435/) (2025)
- [Agent Identity Evals: Measuring Agentic Identity](https://mlsanity.com/paper/2507.17257/) (2025)
- [ContextEcho: A Benchmark for Persona Drift in Long Agentic-Coding Sessions](https://mlsanity.com/paper/2605.24279/) (2026)
- [When Attention Closes: How LLMs Lose the Thread in Multi-Turn Interaction](https://mlsanity.com/paper/2605.12922/) (2026)
- [Directed Metric Structures arising in Large Language Models](https://mlsanity.com/paper/2405.12264/) (2024)
- [Is magnitude 'generically continuous' for finite metric spaces?](https://mlsanity.com/paper/2501.08745/) (2025)
- [Nautilus Compass: Black-box Persona Drift Detection for Production LLM Agents](https://mlsanity.com/paper/2605.09863/) (2026)

## Abstract (arXiv)

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 √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 Sn 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.