Supplement to: The Agent Telephone Game (2026)

Abstract This supplement extends the "Agent Telephone Game" framework by examining ultra-long context windows as a critical engineering mitigation for information decay in autonomous systems. While the original paper identified iterative lossy compression as the root cause of progressive precision loss in multi-step agent chains, this work analyzes the recent deployment of Google’s Gemini-based agents as a real-world case study. We argue that by expanding the operational context to $10^{6}$ tokens and beyond, these systems transition from a "summarize-and-pass" paradigm to a "near-lossless persistence" model. This architectural shift effectively flattens the cumulative distortion curve, providing empirical validation that preserving raw intermediate states is the most viable contemporary defense against semantic drift in complex, long-horizon AI workflows. Keywords Large Language Models (LLMs); Autonomous Agents; Information Theory; Long-Context Window; Semantic Compression; Multi-Agent Systems (MAS); Gemini 3; Information Decay. JEL Classification C63 - Computational Techniques; Simulation Methods (relating to agent-based modeling). D83 - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness. O33 - Technological Change: Choices and Consequences; Diffusion Processes.