Measuring the engine of a liquidation cascade: subcritical branching inside a first-order transition

Abstract

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.