Recursive Drift in Federated AI Systems: A Formal Model of Systemic Semantic Error in Multi-Service Architectures

This paper introduces a formal model for a novel class of systemic error in modern data systems: API-Recursive Drift. I argue that in federated data architectures, where services communicate via Application Programming Interfaces (APIs), each API call acts as a recursive step that can introduce and amplify small, non-malicious errors. The model, grounded in an information-theoretic framework, quantifies this drift as a function of system parameters including initial data integrity (I), model maturity (M), and a newly proposed "API Translation Error" parameter (ψ). This work generalizes the "model collapse" phenomenon to complex, multi-service systems and distinguishes this architectural vulnerability from traditional adversarial attacks and model hallucinations. The paper includes agent-based simulations to explore the model's dynamics and concludes with a set of practical, architectural guidelines for designing and implementing more resilient, high-fidelity AI systems. This research provides a quantitative framework for understanding and mitigating systemic error in any organization building complex, federated data pipelines.