测量清算级联的引擎：一阶相变内部的次临界分支
Measuring the engine of a liquidation cascade: subcritical branching inside a first-order transition
中文总结 AI 辅助
该研究分析2022-2025年7次加密永续合约清算级联，发现其为深度次临界一阶相变，排除Galton-Watson级联模型，揭示清算严重程度由冲击、路径映射与流动性撤资共同决定。
中文摘要 AI 辅助
我们研究了2022-2025年间的7次主要加密永续合约清算级联，其中最大的一次使我们能够直接观测其机制。我们从完全透明交易场所的链上成交日志中，实时测量了该事件——2025年10月的崩盘（创纪录的最大规模）——的分支比，且该分支比的两个因素均可观测，无自由常数。该级联处于深度次临界状态：结构比率和放大记账均显示其全程的λ帽约为0.1-0.2，而第三种基于流的估计器在峰值阶段下降而非上升。三者均一致认为该交易场所内部存在次临界性，但在共同数值水平上存在差异。与此同时，88%的崩盘后强制平仓发生在30分钟内，其中63%被交易场所的后盾（backstop）账外吸收，这恰好使峰值阶段的分支比下降。在全部7次事件中，在崩盘起始点（每次崩盘最剧烈小时结束的分钟），序参量（资产间平均耦合）跃变1.6至4.4个基线标准差，进入近完全有序相，而 susceptibility代理χ在7次事件中的5次中崩溃，无一次发散；该跃变在子抽样下不变。该转变是突变且尺度稳健的，而非临界转变，其级联内特征存在于流动性领域：2个交易场所和2种工具的价格影响飙升，而未平仓合约（open interest）平仓25-70%。随后，我们排除了Galton-Watson级联（λ=kρ~）作为崩盘前状态的描述：其两个可证伪预测在模拟功效≥0.96时失效，无论是代理回归量还是直接测量回归量均如此。严重程度由冲击×路径映射×流动性撤资决定，而非发散乘数，这就是我们构建的所有标量预状态指标均无法对其进行分级的原因。
英文摘要
We study seven major crypto-perpetual liquidation cascades (2022-2025), and in the largest of them we can watch the mechanism directly. From the on-chain fill log of a fully transparent venue we measure the branching ratio of that event -- the October 2025 crash, the largest on record -- in flight, with both of its factors observed and no free constants. It ran deeply subcritical: the structural ratio and the amplification bookkeeping both place it at $\hatλ\approx 0.1-0.2$ throughout, while a third, flow-based estimator falls through the climax rather than rising. All three agree on subcriticality within the venue, not on a common numerical level. Alongside them, 88% of all post-onset forced selling landed within thirty minutes and 63% of it was absorbed off-book by the venue's backstop, which drives the branching ratio down precisely at the climax. Across the full set of seven, at onset -- the minute ending the steepest hour of each crash -- the order parameter (mean inter-asset coupling) jumps by between 1.6 and 4.4 baseline standard deviations into a near-fully-ordered phase, while the susceptibility proxy $χ$ collapses in five of the seven events and diverges in none; the jump is invariant under subsampling. The transition is abrupt and scale-robust rather than critical, and its in-cascade signature lives in the liquidity sector: price impact spikes on two venues and two instruments while open interest clears by 25-70%. The natural mechanistic account, a Galton-Watson cascade with $λ= k \tildeρ$, is then eliminated as a description of the pre-cascade state: both of its falsifiable predictions fail at simulated power >= 0.96, on proxied and on directly measured regressors alike. Severity is set by shock times map-in-path times liquidity withdrawal rather than by a diverging multiplier, which is why none of the scalar pre-state measures we can construct grades it.
