This preprint investigates the physical mechanism behind abrupt critical transitions—such as liquidity collapses—in information-driven macroscopic systems. By analyzing the near-threshold sector of a non-Hermitian information-fluid operator, we find that these sudden market collapses correspond to a topological singular regime governed by exceptional-point (EP) geometry. Specifically, as the Fisher information metric of the underlying statistical manifold approaches degeneracy, two fluctuation modes coalesce. This causes the macroscopic susceptibility to exhibit the square-root branch-point structure typical of a second-order exceptional point. We test this theoretically derived scaling law against high-frequency empirical data. Using 5.28 million millisecond-resolution trades from the BTC/USDT liquidity collapse on 5 August 2024, we show that the predicted scaling holds across three decades. An independent event on 13 April 2024 yields the exact same exponent. These findings suggest that non-Hermitian geometric degeneracy provides a concrete, topology-constrained mechanism for critical transitions in financial order flows.
Chao Ma (Sat,) studied this question.