Toward a Unified Geometric Theory of Multi‑Agent Systems

This work introduces the first unified geometric framework for analyzing drift, divergence, and collapse in multi‑agent AI systems. Building on the layered interpretive ontology developed in *Interpretive Dynamics* (Ecker‑Fils, 2026), the paper models each agent as a stratified manifold equipped with syntactic, execution, boundary, and applicability layers. Multi‑agent interaction is expressed through cross‑agent coupling tensors, and system‑level instability is captured through a generalized collapse taxonomy and a multi‑agent collapse‑risk functional.

A central contribution of this work is the integration of anchor‑based relative geometry (Moschella et al., 2023; Kucukahmetler et al., 2026), which provides the invariant latent substrate required to operationalize interpretive geometry across heterogeneous agents. Relative embeddings quotient out rotations, scalings, and seed‑level distortions, enabling geometry‑aware diagnostics that reveal latent instability long before behavioral divergence becomes observable. This empirical substrate completes the theoretical program initiated in *Interpretive Dynamics*, transforming the framework from a purely geometric theory into a practical methodology for monitoring and stabilizing distributed interpretive systems.

The paper situates itself within and extends several research traditions, including representation learning, multi‑agent systems, cybernetics, and alignment theory. It offers a predictive alternative to heuristic monitoring by grounding multi‑agent behavior in curvature, coupling, dissipation, and observability. The resulting framework is architecture‑agnostic and applies equally to LLM‑based agent ecosystems, heterogeneous forecasting ensembles, hybrid symbolic‑neural pipelines, and other distributed interpretive systems.

This work is intended for researchers in AI safety, multi‑agent coordination, representation learning, and systems design, as well as for practitioners seeking principled tools for diagnosing and mitigating instability in complex agentic ecosystems. It provides both the conceptual foundations and the operational substrate for a new field: multi‑agent interpretive geometry.