Critical slowing
Derived Derived. Corroborating, not deciding (convention C2). Drift-derived indicators are hard to estimate near the transition.
Source: Style sheet v22 §1.5
Definition (canon)
τ↑, variance↑, lag-1 autocorrelation → 1. The fold-type precursor.
Estimability caveat (canon, §1.5). Fitting a drift–diffusion–jump model to series approaching a known transition, total variance is the most precisely estimated indicator and improves with sampling frequency; drift-derived indicators (autocorrelation, return rate, any eigenvalue built from them) are imprecise, degrade further near the transition, and are not rescued by faster sampling (Carpenter & Brock, 2011).
In plain words
Near the edge, the system takes longer to settle after a push, and it wanders more.
It is not
- Proof of a loop. Slowing needs no loop: a saturating step slows anyway. See queue.
- A decider. The sign of the recovery-time trend corroborates a typing and does not decide it (C2). More robust is whether divergence occurs at all.
What would defeat it
- Follows from the definition. A node typed fold that approaches its transition with no slowing under a quasi-static sweep.
- Canon. A sweep rate that is too fast can erase slowing that is really there. The two-rate test (run at two rates an order of magnitude apart) is the check.
Where it is carried
Ledger rows
- L07 Simulated Sweeping the knob too fast mistypes a fold as a hinge: the apparent exponent is biased low (0.117 to 0.393 against a true 0.5). In collapsed units the bias is a calibration known in advance.