Hysteresis-Aware Exit Criterion¶

Exit rule — instantiates Stock-First Control Restoration

Sets the bar for declaring 'back to normal' higher than the bar at which control failed — because a recovering system re-crosses its disabled boundary along a different path than it fell.

The last mistake in a restoration is declaring victory too early. Hysteresis-Aware Exit Criterion is the rule that decides when to fully exit the stock-first regime and hand control back to the ordinary lever — and it sets that exit threshold with margin beyond the point where control originally failed. Its distinguishing idea is a flat refusal of the symmetry assumption: "we failed at X, so we're safe again at X" is false whenever recovery follows a different path than collapse. The criterion treats the disabled-control boundary as a loop, not a line — two thresholds, a lower one for falling in and a stricter one for climbing out — and it will not authorize normal operation until the system has cleared the stricter one and held there.

Example¶

A shallow lake flips from clear to turbid when nutrient loading pushes phosphorus past a tipping point; managers cut the nutrient inputs to bring it back. But shallow lakes are famously hysteretic: the phosphorus level needed to recover clarity sits well below the level at which the lake tipped, because sediment keeps releasing stored phosphorus and the recovery path lags. A Hysteresis-Aware Exit Criterion refuses to call the lake "restored" — and refuses to relax nutrient controls back to normal — the moment phosphorus merely dips beneath the original tipping point. It requires phosphorus to fall well under that point, with clarity sustained across seasons, before normal loading resumes. Exit at the symmetric mark and the lake simply flips straight back to turbid; the margin is the whole point.

How it works¶

It manages the boundary as a two-threshold loop and guards the climb back out:

Place the exit threshold beyond the failure threshold. Offset it by a margin sized to the observed hysteresis, not to the point where things broke.
Require sustained, not instantaneous, recovery. The state must hold past the exit threshold across a dwell window, so a momentary touch doesn't trigger a premature release.
Only then authorize full restoration. It is the final gate — the one standing between "the lever works again in a probe" and "the lever is trusted at full strength."

Where the earlier gates ask can we start?, this one asks are we durably out?

Tuning parameters¶

Hysteresis margin — how far beyond the failure point the exit bar sits. A wide margin makes relapse very unlikely but prolongs the special regime; a narrow one resumes normal operation sooner at the risk of a flip-back.
Dwell requirement — how long recovery must hold before exit. Longer dwells catch slow relapse; shorter ones exit faster.
Boundary estimate source — how the failure and recovery thresholds are known (history, model, probing). A bad estimate mis-places both bars at once.
Relapse response — what happens if the criterion is met and the system slips anyway: re-enter safe mode, re-lock the lever, or re-open repair. Aggressive re-entry is safe but costly.

When it helps, and when it misleads¶

Its strength is that it prevents the most seductive late-stage error — resuming normal control the instant the metric crosses back over the failure line — which, in a hysteretic system, drops you straight back into collapse. It makes "recovered" mean durably recovered rather than momentarily recovered.

Its failure mode is a mis-estimated loop: overstate the hysteresis and you hold the system in an unnecessary special regime far too long; understate it and you exit into a relapse. The classic misuse is quietly sliding the exit bar down toward the failure point to declare recovery on schedule — discarding the very margin the criterion exists to enforce. The discipline is to fix the hysteresis margin and dwell from evidence before recovery is in sight, and to treat any downward adjustment as a decision requiring the same authority as the original diagnosis. The property it respects is hysteresis — a system whose state depends on its history, so the driving variable must be pushed well past the original threshold to reverse the change.^[1]

How it implements the components¶

Hysteresis-Aware Exit Criterion fills the exit-gating side of the archetype — the components that decide when the special regime ends:

hysteresis_exit_check — it is the test that recovery has cleared the failure point by a hysteresis-sized margin and held there.
disabled_control_boundary — it treats that boundary as a two-threshold loop and sets the stricter crossing for the way out.

It does not verify the first re-coupling (coupling_probe — Low-Amplitude Reactivation Probe) or gate the initial restart on stock level (repair_threshold — Deleverage-Before-Stimulus Rule); it governs only the final exit.

Instantiates: Stock-First Control Restoration — this rule is the durable-recovery gate that ends the restoration cleanly.
Consumes: Staged Lever Ramp — the exit criterion closes out a resume already in progress.
Sibling mechanisms: Low-Amplitude Reactivation Probe · Staged Lever Ramp · Gain-Collapse Test · Lever Freeze-or-Cap · Fallback Control Mode · Deleverage-Before-Stimulus Rule · Minimum Stock-Floor Alert · Replenishment-or-Refill Protocol · Substrate Repair Protocol · Stock-Flow Diagnostic Map · Trust-Repair-Before-Persuasion Rule

Notes¶

Without the hysteresis margin, a system that keeps exiting at its failure point will oscillate in and out of the disabled regime — a costly limit cycle of recover-relapse-recover. The margin is what converts a one-time recovery into a stable one, which is why this gate, though last, is what makes the whole archetype robust to repeated shocks rather than merely to the first.

References¶

[1] Hysteresis — a property whereby a system's current state depends on its past, so its recovery path differs from its collapse path and the driving variable must be pushed well beyond the original tipping point to reverse the change. Common in ecological regime shifts such as shallow-lake eutrophication. ↩