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.

pith.paper-citation-record.v1
2411.15088 v1

Coverage vector

measured 55 of 55 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T14:37:07.525555Z

measured 56 of 56 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-12T04:39:38.026979Z

measured 0 of 1 external citation measurements

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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+00:00.

Observation 27381763-5dac-4a36-b304-a2f2df6e8209 · outbound

This paper cites 1, 45–50.

Structure of the chromatic polynomial 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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+00:00.

Observation 713247f3-feef-4ea2-994b-3d17ed8dfaf5 · outbound

This paper cites 1, 77–88.

Structure of the chromatic polynomial 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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+00:00.