Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T11:50:43.035226Z
Paper Citation Record · LEDGER
An equality for balanced digraphs
As of 8 August 2026, this Paper Citation Record lists 8 of 8 outbound references and 0 inbound Pith citation observations for arXiv:2507.22388.
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 2026-08-08T06:32:00.761636+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
8 of 8 outbound references displayed
- verified exact3
- verified fuzzy0
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch2
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b0301c11-ac7f-4adf-a278-051ac697ed69 · outbound
This paper cites An introduction to graph theory.
An equality for balanced digraphs An introduction to graph theory
Reference 1
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-06T11:50:44.029476Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2e1f36c0-88a3-4851-b2eb-4834c61f72a1 · outbound
This paper cites https://doi.org/10.1007/978-3-319-71840-8.
An equality for balanced digraphs https://doi.org/10.1007/978-3-319-71840-8
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T11:50:42.479614Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 944c2ac8-9079-492f-9ead-2c25101c6f1d · outbound
This paper cites Bialgebras in cointeraction, the antipode and the eulerian idempotent.
An equality for balanced digraphs Bialgebras in cointeraction, the antipode and the eulerian idempotent
Reference 3
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T11:50:43.856783Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e8966ea7-5726-4b83-9de4-eaf5168d0410 · outbound
This paper cites an unresolved cited work.
An equality for balanced digraphs Unresolved cited work
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T11:50:42.693044Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5703f49a-7c09-4309-8f9a-056314732063 · outbound
This paper cites Computing the EHZ capacity is NP-hard.
An equality for balanced digraphs Computing the EHZ capacity is NP-hard
Reference 5
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-06T11:50:43.676864Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation cb3ae720-5b8a-42dd-b7f2-43e589fa46ba · outbound
This paper cites an unresolved cited work.
An equality for balanced digraphs Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T11:50:44.243288Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 9bb63314-794c-4b13-8fcb-4b8efde7b64c · outbound
This paper cites On the complexity of counting feedback arc sets.
An equality for balanced digraphs On the complexity of counting feedback arc sets
Reference 7
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T11:50:43.467152Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3ba2c003-1aca-4a7b-8d88-e2a02c569900 · outbound
This paper cites https://doi.org/10.1007/978-1-4612-4968-9.
An equality for balanced digraphs https://doi.org/10.1007/978-1-4612-4968-9
Reference 8
- Resolution
- verified exact
- doi, observed 2026-08-06T11:50:43.224772Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Pith citing papers
No inbound Pith citation observations are available.