Synchronization Reveals Market Structure That Classical Randomness Tests Cannot Detect

Abstract: Synchronization among coupled oscillators -- from firing neurons to flashing fireflies to power grids -- is a universal signature of collective behavior in complex systems, and is classically measured by the Kuramoto order parameter. Financial markets have been proposed as another such system, with price dynamics across trading timescales treated as coupled oscillators; prior work applying this measure, however, has been confined to a single asset class, and has never been checked against the discipline's own classical diagnostic for structure, the random-walk hypothesis. Here we show that a Kuramoto-style coherence measure, applied identically across five asset classes and 61 financial instruments -- cryptocurrency, foreign exchange, metals, equity indices, and single-name equities -- detects structure that a calibrated, heteroskedasticity-robust variance-ratio test of the random-walk hypothesis does not: the two diagnostics are statistically independent of one another even when computed from the same price history on the same time windows. The coherence measure tracks the directional cleanliness of recent price moves universally across all five asset classes, and offers a modest, asset-class-dependent forecast of future move magnitude -- strongest in continuously-traded, momentum-prone markets -- while the variance-ratio test finds the same panel statistically indistinguishable from a random walk in the large majority of cases. This independence indicates that a physics-derived synchronization diagnostic accesses a layer of structure that a discipline-native statistical test cannot, a methodological lesson we expect generalizes to other complex systems where tools imported from physics are compared against a field's own classical null-hypothesis tests.