Horizon Intelligence Quotient: A Psychometric Frame work for Measuring, Benchmarking, and Interpreting Ma chine Intelligence

Existing AI evaluation frameworks report raw accuracy figures that resist comparison across tasks, time, and system generations. We present the Horizon Intelligence Quotient (HIQ) framework: a psychometrically principled system that converts raw Brier Skill Score performance into an interpretable normed scale (mean 100, SD 15) via HIQ = 100 + 15 (Φ-m)/s. The framework has four components. First, the Meridian model decomposes machine forecasting performance into four orthogonal skill components: Reach, Efficiency, Adaptivity, and Breadth, yielding a multi-dimensional profile that scalar benchmarks cannot provide. Second, closed-form standard error and Spearman-Brown reliability formulas bound measurement precision at any question budget, enabling principled sample size planning. Third, we identify and quantify four validity threats: benchmark contamination (∆HIQ = 408δ), stale norm drift (3.03.75 HIQ points per year), forking-path inattention, and Adaptivity Inversion, and provide analytic corrections for each. Fourth, we estimate the HIQ reference norm empirically for the first time using leave-one-out cross-validation (LOO-CV) on five AI systems from Halawi et al. (2024), yielding pilot norm ˆm = 0.1264, ˆs = 0.0321 with jackknife standard errors eliminating the circularity of scoring systems against a norm derived from themselves. LOO-CV scores range from HIQ = 60.1 (Gemini Pro) to 130.6 (GPT-4-1106); pipeline portability is confirmed by independent replication on ForecastBench (Karger et al., 2025).