Passing min_score to elastic in query

Assuming that the response from @JasonStoltz in this question:

is the same response I'll get here regarding the min_score function. To @JasonStoltz or someone else who's knowledgable... I can solve the problem of truncating the search results at some score on my end pretty easily. Is there a way to solve the 2nd problem I mentioned above regarding getting facets and counts that apply to a shorter result list?