Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-12T14:37:07.525555Z
Paper Citation Record · LEDGER
Structure of the chromatic polynomial
As of 18 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 1 inbound Pith citation observation for arXiv:2411.15088.
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 2026-08-17T06:30:58.91139+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-12T04:39:38.026979Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-12T04:39:38.342078Z
Reference resolution
55 of 55 outbound references displayed
- verified exact0
- verified fuzzy30
- unresolved25
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 029add68-53f6-44d7-9868-a78c1bda5979 · outbound
This paper cites 1, 201–206.
Structure of the chromatic polynomial 1, 201–206
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:09.586076Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 38e2f28b-20fc-4353-bfc3-5232ebeab9ac · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:09.541728Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation b28427b8-b64a-4e54-a6e0-5f692f103d66 · outbound
This paper cites 1-2, 97–120.
Structure of the chromatic polynomial 1-2, 97–120
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:09.508240Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 00cfae0a-ed82-440f-802f-5543a8a7da82 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:09.475881Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation a1b3de73-1e02-46ab-ac32-dfbdcef87994 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:09.448659Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 24d6ff95-f3fc-4976-818c-a33139ab6c53 · outbound
This paper cites 1, 179–189.
Structure of the chromatic polynomial 1, 179–189
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:09.405129Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation e36e4992-6306-4ac2-ba0e-e28a0ab9f76e · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:09.356190Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 8a478ffb-a33a-451e-b1d7-ee422744ae64 · outbound
This paper cites 2, 320–345.
Structure of the chromatic polynomial 2, 320–345
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:09.323634Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation c92c0e38-1fa1-4ba9-9c40-d45a325b404b · outbound
This paper cites 2, 139–143.
Structure of the chromatic polynomial 2, 139–143
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:09.284510Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation b9366d2d-b141-4e3e-85a1-b5c905669905 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:09.255654Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation faed0d5b-27ba-47a8-94b2-ad78ff9056e4 · outbound
This paper cites 2, 171–177.
Structure of the chromatic polynomial 2, 171–177
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:09.223533Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 133aa1ad-a470-41ff-b81e-c7991d725d52 · outbound
This paper cites Nikiforov , Discrete Mathematics 309 (2009), no.
Structure of the chromatic polynomial Nikiforov , Discrete Mathematics 309 (2009), no
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:09.173283Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation f0747da5-3967-4894-8444-03aa0886958e · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:09.148709Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation e4102aa5-434c-4854-9781-4e0df7ca76c8 · outbound
This paper cites 4, 261–284.
Structure of the chromatic polynomial 4, 261–284
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:09.117791Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation f20494c9-95dc-427c-8550-ae396d3825dc · outbound
This paper cites The signature and cusp geometry of hyperbolic knots.
Structure of the chromatic polynomial The signature and cusp geometry of hyperbolic knots
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T14:37:07.114222Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation da407de3-cd2f-4b92-8e12-8339ec35e1da · outbound
This paper cites 7887, 70–74.
Structure of the chromatic polynomial 7887, 70–74
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:09.080998Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 27381763-5dac-4a36-b304-a2f2df6e8209 · outbound
This paper cites 1, 45–50.
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:09.051797Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation d9511ece-6b36-477f-bdd4-6d2a8d32e9a1 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:09.006726Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 8089b468-3974-4281-a002-d78615f378e2 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:08.966036Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation d4e395f5-3244-46ef-9c29-f92de5145b92 · outbound
This paper cites 6, 1553–1560.
Structure of the chromatic polynomial 6, 1553–1560
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.937833Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation e0cbe9ec-8e80-479b-8657-313100b2a052 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:08.894234Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 1b5a996d-5538-435b-b3d9-afd585efa29a · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:08.856339Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 0adb3d4d-124b-4f4b-84c7-42c98815f042 · outbound
This paper cites 4, 1365–1388.
Structure of the chromatic polynomial 4, 1365–1388
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.825263Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 89c4ad34-9a2c-4b59-9b14-e8f770193013 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:08.799988Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 3ffba744-d41c-4128-8123-d54f0a601a3b · outbound
This paper cites 03, 2050005.
Structure of the chromatic polynomial 03, 2050005
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.771855Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 99a78ec8-9302-4e6d-8e11-0147b763594a · outbound
This paper cites 3, 907–927.
Structure of the chromatic polynomial 3, 907–927
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.729856Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 7a627cd9-7783-4639-bacc-aa1a9b576027 · outbound
This paper cites 20 RADMILA SAZDANOVIC AND DANIEL SCOFIELD.
Structure of the chromatic polynomial 20 RADMILA SAZDANOVIC AND DANIEL SCOFIELD
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.690661Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation e7b4ef90-cbe8-4c85-9406-36f2b8b5b775 · outbound
This paper cites 2065, 20150202.
Structure of the chromatic polynomial 2065, 20150202
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.648034Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 97e1a94e-f21f-4398-8873-dc93f8b5de77 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:08.617430Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 9c1ad0dc-968e-485a-a45c-4c54c7aa49f3 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:08.589989Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 713247f3-feef-4ea2-994b-3d17ed8dfaf5 · outbound
This paper cites 1, 77–88.
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.542903Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 838a1f9c-46f8-4ebe-ba84-15578fd6597b · outbound
This paper cites 6, 703–723.
Structure of the chromatic polynomial 6, 703–723
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.508174Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 54ae1215-f0f3-4202-9ae8-30210e5024d5 · outbound
This paper cites 10, 2783–2791.
Structure of the chromatic polynomial 10, 2783–2791
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.460991Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 04d68c4e-06be-479d-9c66-0c8d4aa1a23b · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:08.417515Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 8d676cfc-4033-404a-8993-be9dea4f78a8 · outbound
This paper cites Big Data Approaches to Knot Theory: Understanding the Structure of the Jones Polynomial.
Structure of the chromatic polynomial Big Data Approaches to Knot Theory: Understanding the Structure of the Jones Polynomial
Reference 36
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T14:37:07.332822Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f4a8e6ca-2607-412c-a4c3-dd0fd86ae71e · outbound
This paper cites 1-3, 181–185.
Structure of the chromatic polynomial 1-3, 181–185
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.385377Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation b07aa157-a6e8-49d7-a88c-fcd8bf7e4bea · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:08.328740Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation c35afab9-182a-4268-9fb0-b14c564fb022 · outbound
This paper cites 1, 347–360.
Structure of the chromatic polynomial 1, 347–360
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.292507Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 69d05eaa-f02b-45f2-9b62-3b7c23b2cb34 · outbound
This paper cites 2, 365–384.
Structure of the chromatic polynomial 2, 365–384
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.232650Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 2dd69d05-c4f5-4592-93a9-a848ecd6bb6d · outbound
This paper cites 3, 383–398.
Structure of the chromatic polynomial 3, 383–398
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.197254Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 709352be-29f6-4fdd-9740-f40fce299eac · outbound
This paper cites Ball mapper: a shape summary for topological data analysis.
Structure of the chromatic polynomial Ball mapper: a shape summary for topological data analysis
Reference 42
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T14:37:07.375948Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 930169f3-4ffe-447a-b515-9b7f93190730 · outbound
This paper cites Mapper-type algorithms for complex data and relations.
Structure of the chromatic polynomial Mapper-type algorithms for complex data and relations
Reference 43
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T14:37:07.381693Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a94b13d3-34bf-4ee4-b5b7-5f2200dbdc84 · outbound
This paper cites Pedregosa, G.
Structure of the chromatic polynomial Pedregosa, G
Reference 44
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.166875Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation d162493d-df85-438a-97d7-306895b388af · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 45
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:08.138580Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation afd6d8a6-dfe8-4b01-8d24-1107973d71e1 · outbound
This paper cites 1-3, 115–119.
Structure of the chromatic polynomial 1-3, 115–119
Reference 46
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.112469Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 94485ce0-2c4b-41af-ab34-a75994105b07 · outbound
This paper cites Theory of M¨ obius functions, Zeitschrift f¨ ur Wahrscheinlichkeitstheorie und verwandte Gebiete2 (1964), no.
Structure of the chromatic polynomial Theory of M¨ obius functions, Zeitschrift f¨ ur Wahrscheinlichkeitstheorie und verwandte Gebiete2 (1964), no
Reference 47
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.078055Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation b520cfb1-392e-46b9-91ce-62c1ece12c0d · outbound
This paper cites 2, 209– 216.
Structure of the chromatic polynomial 2, 209– 216
Reference 48
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:08.027471Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation fde9e08d-a242-4ea0-aa72-e9494db8895a · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 49
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:07.988834Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation dbfa5624-63a2-44d2-81f4-1d19cf0c1134 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 50
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:07.945765Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 8d3608c3-6b9c-4de7-8f4a-f71362e31e28 · outbound
This paper cites 1, 166–194.
Structure of the chromatic polynomial 1, 166–194
Reference 51
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:07.907393Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 86cb6055-1fe9-4ab8-a048-391ecb486cb0 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 52
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:07.851875Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation ad7156a9-2455-419c-840a-e46da9c6672a · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 53
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:07.813311Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation b5d4b75d-7a0f-4e44-838b-ebf508c4d669 · outbound
This paper cites an unresolved cited work.
Structure of the chromatic polynomial Unresolved cited work
Reference 54
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T14:37:07.786632Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 4756df98-085a-48e0-9210-16587a8f4dd6 · outbound
This paper cites 21(1), Springer, 1957, pp.
Structure of the chromatic polynomial 21(1), Springer, 1957, pp
Reference 55
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:07.766699Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 123bf3d7-e968-4b8c-a8a5-89f39de6b890 · outbound
This paper cites 8, 572–579.
Structure of the chromatic polynomial 8, 572–579
Reference 56
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T14:37:07.744197Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Pith citing papers
Observation a64b2a59-3ce8-4351-8286-2cd117fee3f2 · inbound
Big data approach to Kazhdan-Lusztig polynomials cites this paper.
Big data approach to Kazhdan-Lusztig polynomials Structure of the chromatic polynomial
Reference 52
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T04:39:38.345673Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.