Admissible
Which cut positions a run of equal values rules out.
This is about ties, and only about ties. A partition is defined by intervals of value, so observations that are equal must stay in the same group; a position inside a run of equal values is therefore not a position at all. That is the whole of what AdmissibilityCertificate decides per position — the minimum group size and the minimum distinct count are properties of a whole partition rather than of a single cut, and are not what this figure shows.
On continuous data it has nothing to say, because every observation is distinct and no position is ruled out. Check hasRefusedPositions before drawing it: a figure in which every mark is the same colour tells a reader nothing and invites them to think it is broken. It earns its place on data that has been rounded or recorded to a coarse unit, which is common enough in service-time data to be worth having.
Parameters
the sample, which need not be sorted
the admissibility certificate for that sample
what the observations measure, for the axis label