Paper Citation Record · LEDGER

Cover numbers by certain graph families

As of 12 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 1 inbound Pith citation observation for arXiv:2412.08980.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.08980 v2

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T17:37:09.516094Z

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T00:27:56.873485Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-11T00:27:56.948714Z

Reference resolution

10 of 10 outbound references displayed

verified exact0
verified fuzzy1
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2116a05b-bd95-487b-9f8f-46627589af8a · outbound

This paper cites an unresolved cited work.

Cover numbers by certain graph families Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:37:09.787086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 80817605-f0e4-4992-9ba7-6e9c0d1cdab7 · outbound

This paper cites an unresolved cited work.

Cover numbers by certain graph families Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:37:09.770719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 19128a65-d371-4274-8207-d9c43aceb904 · outbound

This paper cites an unresolved cited work.

Cover numbers by certain graph families Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-11T17:37:09.470493Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc37a2d1-70d4-4dec-81dd-a6b1dc8ae663 · outbound

This paper cites an unresolved cited work.

Cover numbers by certain graph families Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:37:09.753568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e01fae1b-8f78-448b-9bae-82085ba8cee2 · outbound

This paper cites an unresolved cited work.

Cover numbers by certain graph families Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:37:09.736237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3c181bf4-7473-4b99-9f18-93f6d865f787 · outbound

This paper cites an unresolved cited work.

Cover numbers by certain graph families Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:37:09.719945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 184315b4-b796-453e-8ef5-00ee220d478d · outbound

This paper cites an unresolved cited work.

Cover numbers by certain graph families Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:37:09.704377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation dd066bff-499f-4450-84de-3f50d41ba436 · outbound

This paper cites J., & Steger, A.

Cover numbers by certain graph families J., & Steger, A

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:37:09.689843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c1244302-f5ce-4092-913a-b8a788ea5b05 · outbound

This paper cites an unresolved cited work.

Cover numbers by certain graph families Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:37:09.674858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c26263a5-b13d-48ca-8a24-7e6313bf9da2 · outbound

This paper cites an unresolved cited work.

Cover numbers by certain graph families Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-11T17:37:09.657611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation 9f3e778a-4115-4986-980c-bfe941f9ff3d · inbound

Boolean combinations of graphs cites this paper.

Boolean combinations of graphs Cover numbers by certain graph families

Reference 1972

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:27:56.957373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.