count Adequacy
Whether this sample is large enough for the recommended component count to be answerable at all, or null when the question does not arise.
Read this before the count, not after it. The component count is the least reliable thing this class reports, and how reliable it can possibly be is governed by the sample size and by how far the fitted mixture sits from the nearest mixture with one component fewer. Where that product is small, no procedure could settle the question and the number below is close to a guess.
Null when the recommendation has a single component, since there is then no count to settle, and null when the separability could not be computed — reported as absent rather than as an adequate or inadequate verdict.
Computed on demand rather than eagerly: it costs one minimisation over the fitted mixture, which is far cheaper than a bootstrap but not free.