The Golden Ratio "Conservation Law" in Artificial Intelligence: An Empirical Discovery

Hyperparameter tuning in modern AI systems—such as the exploration parameter c_puct in Monte Carlo Tree Search and Temperature in large language models—remains largely empirical. Through meta-evolution experiments on a Chess AI system (5,060+ generations) and cross-validation on 10 state-of-the-art systems, we discovered a potentially universal pattern: exploration parameters appear to follow a "conservation law" based on the golden ratio. Specifically, we found that energy levels tend to converge to quantized values, predominantly 6.854. Recent empirical work by DeepSeek validates our theoretical predictions: their optimal 75/25 thinking-memory allocation precisely matches our derived ratio of phi^2:1. We further predict that DeepSeek-V4, rumored to adopt CPU-based thinking, should use Temperature approx 0.0-0.10