Precursor cascade (corrected)
Simulated Derived and simulated in a mean-field bundle. The old pairing with the hinge is withdrawn.
Source: Style sheet v22 §1.5 (as corrected at v16; erratum of 2026-11-06)
Definition (canon)
Clustering small events with power-law size distribution. Not a node type's precursor — corrected at v16, where this read the hinge-type precursor. A cascade is a property of a coupled population whose round-trip gain approaches one: a burst is a branching cascade with branching ratio G, mean size 1/(1 − G), giving P(S) ∝ S^(−3/2) at G = 1. It is therefore produced by a fold at the population scale and types the coupling one scale below, not the node at the transition.
A cascade is not exclusive to any constituent type. It needs discrete threshold-like transitions, coupling, and gain near one. What the event stream can type is the constituents, read off reversibility.
In plain words
When many linked parts are each close to tipping, one event sets off others in a chain. The nearer the whole is to its edge, the longer the chains.
It is not
- A hinge's warning. That pairing was withdrawn on 2026-11-06 after the pressure test fired the original kill test.
- A discriminator on its own. Distinct combinations of geometry and coupling produce the same distribution.
What would defeat it
- Canon, erratum. A mean-field cascade in which the successive-round event ratio departs from the linearised gain by more than finite-N scatter while bursts stay scale-free; or a coupled population at gain approaching one that does not produce scale-free bursts.
See the full erratum.
Where it is carried
- Odd Sympathy Story
Ledger rows
- L05 Withdrawn A hinge announces itself with a scale-free cascade and falling recovery time; a fold with Gaussian fluctuation of rising variance.
- L06 Derived A cascade is the event-stream view of a fold in a coupled population at gain G approaching 1. Mean burst size 1/(1−G); sizes follow S^(−3/2) at G = 1.