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 operating point, appears to have no analogue in the Mandelbrot, Multibrot, or Burning Ship fractal literature. Validated on two live agents: Ocho (prediction markets, Φ = +8.41, n = 94) and Molty (code self-improvement, Φ = +36.61, N = 6). v8 additions: Class C anomalous scaling A(K) ~ πR²/√(ln K) for Gaussian nonlinearities characterised (Remark 3.15); shifted-tanh continuous interpolation (OP-3) confirming smooth Class B → Class A deformation; Ocho’s Law formally named (§4.6.3).