A selection outside the page stayed applied while its checkbox was gone, so
there was no way to remove it. Appending those documents to the page instead
loses the bound the page exists to keep, since selections accumulate across
searches.
Both listings page at `DOCUMENT_PAGE`, and `Selected` switches between them, so
the mounted widgets stay bounded whichever is showing and every selection is a
page away rather than unreachable.
The count reads the checkboxes on screen, so narrowing as the user types reports
what is visible. A listing with nothing in it says so, instead of leaving an
empty box that reads as still loading.
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