Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
Minimum density of union-closed families
As of 14 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:1106.0369.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-11T22:09:03.978071Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-11T22:09:04.359824Z
Reference resolution
0 of 0 outbound references displayed
- verified exact0
- verified fuzzy0
- unresolved0
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
No outbound reference observations are available for this paper version.
Pith citing papers
Observation b548d57e-983f-4849-a235-eb15a5c0912f · inbound
Frequent elements in union-closed set families cites this paper.
Frequent elements in union-closed set families Minimum density of union-closed families
Reference 3
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T22:09:04.368959Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.