Move open risk from eleven to eighteen and the cycle stops being the same kind of cycle.

The sensitivity

One subtraction feeds a comparison, and comparisons have edges.

The chain is smooth until its final test. Remaining capacity falls continuously as open risk rises — eighteen percent, then fifteen, then twelve, then eleven — and per-trade risk falls with it in proportion. Then the comparison against the viability floor resolves, and it resolves as a yes or a no. Above the boundary the cycle runs four fresh trades at whatever compressed size the arithmetic produced. Below it, the default mode stops dividing by four and instead computes how many trades the remaining capacity can support at the minimum viable size, and the count drops. A continuous input has produced a discrete output, and the point at which it flips is a property of the floor rather than of anything the operator did that cycle.

Why the count flexes and not the size

Below the floor, a smaller trade stops being a trade worth taking.

The chain could have continued dividing — three percent, then two, then one — and produced four fresh positions of steadily diminishing consequence. The floor exists to stop it. A trade sized beneath the minimum pays the same fixed friction as a full one while contributing a fraction of the outcome, occupies a slot, and enters the record where it will be averaged alongside properly sized trades. So the design holds per-trade quality constant and lets the count absorb the shortfall, which means a constrained cycle is a shorter cycle rather than a diluted one. That choice is what makes the transition discrete: the moment four viable trades stop fitting, the honest answer is three, and there is no partial state between them.

The unmoved inputs

Nothing about the account's authorisation changed across the boundary.

It is worth being explicit about what did not move, because the outcome invites the assumption that something was demoted. The gate is the same, so capital state is unchanged. The tier is the same, so the authorised pool is still twenty-nine percent and the per-trade ceiling is still whatever the tier permits. The account has not been penalised, restricted or downgraded by any layer of the authority stack. The only thing that changed is how much of the already-authorised budget was still available, and that was determined by trades taken in a previous cycle and by whether their stops have since been advanced. The deployment fell for reasons that live entirely in the operator's own position management.

The other lever

The boundary can be crossed back by moving a stop, not by changing a setting.

Because the input that moved is active risk rather than an authorisation, the route back is also a management action. Advancing the stop on one carryover position from its original level to break-even removes its contribution to open risk entirely, which can be enough on its own to lift remaining capacity back above the boundary and restore the full cycle. That is a materially different situation from being constrained by the gate, where nothing the operator does inside the week changes the ceiling. Here the constraint is downstream of decisions that are still live and still adjustable, which makes checking whether any open position is eligible for a stop advance the first thing worth doing when the count falls.

What the sensitivity teaches

Knowing where the edge sits converts a surprise into a forecast.

The general lesson from running the input across its range is that the boundary has a location and the location is computable from figures already on screen. Given the authorised pool and the viability floor, the maximum open risk compatible with a full cycle is a fixed number for that tier, and an operator who knows it can see the constraint coming. It also explains why exposure pressure read as a series is worth logging: a pressure ratio climbing toward that threshold across several cycles is the same information arriving early. The alternative is discovering the boundary by crossing it, which happens at a deployment decision, under time pressure, with an override switch nearby.

• Continuous input, discrete output — the flip is a property of the floor.
• Count flexes because a sub-viable trade is mostly friction and still enters the record.
• The gate and tier did not move; the constraint came from prior position management.

The key idea

A worked example is worth more when it is run twice.

A single walked case demonstrates that the arithmetic works and teaches very little about how it behaves. Running the same case with one input moved shows where the sensitivities are, which of the steps is smooth and which has an edge, and what an operator would actually have to change to alter the outcome. That is the difference between knowing a chain's formulas and knowing its shape — and the shape is what tells you which number to watch during the cycles when nothing appears to be going wrong.