What does "adjust_pure_negative" flag do?

You can ignore it. It "does the right thing" when calling Lucene when all clauses are "must_not" clauses (no shoulds or musts). Ordinarily Lucene expects some positive clauses so would return nothing. Elasticsearch adjusts for this case by adding a must match_all type clause which means Lucene would then provide results, filtered by the must_nots.
True is the default setting and anything else seems non-sensical.

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