The Aether Equation: A Diagnostic Metric for Autonomous Agent Intelligence Across Domains and Scales

We introduce the Aether Equation Φ(N,t) = (2^N − 1) · BSS · exp(−α|δ̄|), a real-time diagnostic for autonomous agent intelligence calibration. The metric couples Brier Skill Score (BSS), ensemble size (N), and operational bias (δ̄) into a single scalar whose sign separates skillful from unskillful operation. Analysis of the associated parameter-space fractal — the Aether Set, generated by the non-holomorphic iteration z_{n+1} = K z_n g(Im(z_n)) + c — yields an exact two-step stability boundary, a sharp phase transition at K* ≈ 25, and a universal area-decay exponent γ = 2 proved for all nonlinearities g with g(0) > 0. The universality classification γ = 2/(1+α), where α is the order of the zero of g at the…