Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T17:34:16.186566Z
Paper Citation Record · LEDGER
A lemma on a finite union-closed family of finite sets and its applications
As of 14 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2507.11008.
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
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
19 of 19 outbound references displayed
- verified exact4
- verified fuzzy5
- unresolved10
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation fc14a514-cae2-4ea5-8aaa-a64f78974ac3 · outbound
This paper cites an unresolved cited work.
A lemma on a finite union-closed family of finite sets and its applications Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T17:34:16.564338Z
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.
Observation e79716e7-09d0-4bc9-bd20-494b635c834b · outbound
This paper cites 31(6), 2043-2074 (2015).
A lemma on a finite union-closed family of finite sets and its applications 31(6), 2043-2074 (2015)
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T17:34:16.547024Z
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.
Observation a2226614-a35b-45e0-8152-55b0e00dd51f · outbound
This paper cites an unresolved cited work.
A lemma on a finite union-closed family of finite sets and its applications Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T17:34:16.532436Z
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.
Observation 20103597-3ef3-4881-b74d-be5a415196fd · outbound
This paper cites Frequent elements in union-closed set families.
A lemma on a finite union-closed family of finite sets and its applications Frequent elements in union-closed set families
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T17:34:16.356354Z
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.
Observation 8c001ed4-0f54-4356-bb9a-0ec0386b8182 · outbound
This paper cites an unresolved cited work.
A lemma on a finite union-closed family of finite sets and its applications Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T17:34:16.517333Z
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.
Observation 8aa8522b-ea2d-4130-b918-961bbe959cf5 · outbound
This paper cites A constant lower bound for the union-closed sets conjecture.
A lemma on a finite union-closed family of finite sets and its applications A constant lower bound for the union-closed sets conjecture
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T17:34:16.125245Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5274fa63-4d9c-4b88-887c-91ee080dc81d · outbound
This paper cites Sichuan Univ.
A lemma on a finite union-closed family of finite sets and its applications Sichuan Univ
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T17:34:16.501482Z
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.
Observation 5f2974d3-cb8e-4883-89c9-c332324a18fa · outbound
This paper cites The number of abundant elements in union-closed families without small sets.
A lemma on a finite union-closed family of finite sets and its applications The number of abundant elements in union-closed families without small sets
Reference 8
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T17:34:16.313494Z
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.
Observation f6f1f6f0-6efb-4f31-bd09-4bf9f8ae30ee · outbound
This paper cites Two Results on Union-Closed Families.
A lemma on a finite union-closed family of finite sets and its applications Two Results on Union-Closed Families
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T17:34:16.140112Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4cbe6f76-e21f-4356-af07-8f55774642c6 · outbound
This paper cites Improving the Lower Bound for the Union-closed Sets Conjecture via Conditionally IID Coupling.
A lemma on a finite union-closed family of finite sets and its applications Improving the Lower Bound for the Union-closed Sets Conjecture via Conditionally IID Coupling
Reference 10
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T17:34:16.267256Z
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.
Observation 0d4b336f-d16f-473f-a297-c44f4767e2ff · outbound
This paper cites an unresolved cited work.
A lemma on a finite union-closed family of finite sets and its applications Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T17:34:16.486114Z
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.
Observation 9f034ab0-ff82-46b6-8ded-8582edd1f974 · outbound
This paper cites Notes on the Union Closed Sets Conjecture.
A lemma on a finite union-closed family of finite sets and its applications Notes on the Union Closed Sets Conjecture
Reference 12
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T17:34:16.237053Z
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.
Observation e1855756-976e-457d-ade0-b8bab0940204 · outbound
This paper cites an unresolved cited work.
A lemma on a finite union-closed family of finite sets and its applications Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T17:34:16.471737Z
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.
Observation 0cc169e8-63a8-4f47-a8c1-45504f46750a · outbound
This paper cites (Ed.): Graphs and Order, Reidel, Dordrecht/Boston (1985).
A lemma on a finite union-closed family of finite sets and its applications (Ed.): Graphs and Order, Reidel, Dordrecht/Boston (1985)
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T17:34:16.456492Z
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.
Observation 13f4400e-7415-4315-a612-5a0ec4e3ea5a · outbound
This paper cites an unresolved cited work.
A lemma on a finite union-closed family of finite sets and its applications Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T17:34:16.441107Z
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.
Observation 3eb6934f-a767-4dfd-a734-26d471ba4526 · outbound
This paper cites G., Renaud J.-C.: On the union-closed sets conjecture, Ars Combin.
A lemma on a finite union-closed family of finite sets and its applications G., Renaud J.-C.: On the union-closed sets conjecture, Ars Combin
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T17:34:16.424734Z
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.
Observation 114e97b0-ed22-4145-8df5-90e9032eebc8 · outbound
This paper cites P., Enumerative Combinatorics, Vol.
A lemma on a finite union-closed family of finite sets and its applications P., Enumerative Combinatorics, Vol
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T17:34:16.406844Z
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.
Observation 27d8eee1-6001-4f7b-9105-89d71f3e7214 · outbound
This paper cites an unresolved cited work.
A lemma on a finite union-closed family of finite sets and its applications Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T17:34:16.389805Z
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.
Observation f64eb474-1488-4140-a33c-3bd540da5a63 · outbound
This paper cites an unresolved cited work.
A lemma on a finite union-closed family of finite sets and its applications Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T17:34:16.373119Z
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.
Pith citing papers
No inbound Pith citation observations are available.