Within the Strongly Connected Components (SCCs) formed during the temporal evolution of a Cloud permission graph, we use the Burau Lyapunov exponent LE as an algebraic probe to locate the boundary between two risks regimes. We prove that no Abelian statistic (edge counts, net privilege flow, gate-firing rates) can determine LE. The non-commutation advantage is small, but actionable: we show how to leverage it to discriminate the two outstanding risk regimes, that we call dispersed and focused, for automating classification and governing remediation of risky Cloud permission flows.

翻译：在云权限图时序演化过程中形成的强连通分量内，我们采用Burau李雅普诺夫指数LE作为代数探针来定位两种风险状态之间的边界。我们证明任何阿贝尔统计量（边计数、净权限流、门触发率）均无法确定LE。非交换优势虽小但具有可操作性：我们展示了如何利用该优势区分两种显著的风险状态——即分散态与聚焦态，从而实现风险云权限流的自动化分类与治理修复。