Phase Coherence Burst Energy - A Topological Measure of Market Dimensionality and Macro-Shock Decay

Abstract Standard measures of financial correlation — Pearson, PCA, Beta — inherently conflate structural market coupling with asset volatility. During macroeconomic shocks, amplitude spikes trivially inflate these metrics, masking the true geometric degrees of freedom within an equity market. This paper introduces Phase-Coherence Burst Energy, a topological observable that isolates cross-asset structural coupling by extracting the instantaneous Hilbert phase of constituent equities, entirely normalizing out price amplitude. We validate this metric against a rigorous 100-surrogate Iterative Amplitude-Adjusted Fourier Transform (IAAFT) ensemble — a null model that preserves both the exact amplitude distribution and power spectrum of every individual stock while destroying only cross-asset phase alignment. IAAFT validation confirmed exact four-decimal-place preservation of mean, standard deviation, skewness, and kurtosis across all 59 constituents. Applied to 59 S&P 500 mega-cap constituents from 2004 to 2024, we find: (1) real market topology operates at a persistent mean signal-to-null ratio of 2.59×, never once intersecting the 99% IAAFT surrogate envelope across 2,966 observations; (2) peak dimensionality collapses occur episodically at macro-liquidity shocks, with COVID-19 recording the highest Burst Energy in the 20-year sample at 173.3; and (3) shock decay times exhibit a near-monotonic decreasing sequence (p = 0.0085), modulated by peak shock amplitude. We term this structural shift the Hyper-Elastic Market Hypothesis and formalize a falsifiable out-of-sample prediction for the next macro-volatility event.