Paper Citation Record · LEDGER

The Penrose-Kauffman Polynomial

As of 11 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2604.16635.

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

pith.paper-citation-record.v1
2604.16635 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-10T06:49:59.187127Z

measured 19 of 19 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 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

19 of 19 outbound references displayed

verified exact1
verified fuzzy15
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ceb0c9e3-9520-4de6-9706-af828152fe3f · outbound

This paper cites Aigner, The Penrose polynomial of a plane graph, Math.

The Penrose-Kauffman Polynomial Aigner, The Penrose polynomial of a plane graph, Math

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:17.009704Z

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 e8e6ea6c-c83b-490d-ac63-352b97cd2e89 · outbound

This paper cites Quantum state systems that count perfect matchings.

The Penrose-Kauffman Polynomial Quantum state systems that count perfect matchings

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-10T06:51:46.020301Z

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 3b11189e-d06b-499d-8ece-11fada812433 · outbound

This paper cites Biggs, Algebraic Graph Theory, Cambridge University Press, Cam- bridge.

The Penrose-Kauffman Polynomial Biggs, Algebraic Graph Theory, Cambridge University Press, Cam- bridge

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:17.007607Z

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 1d2832cf-cbd5-4fdf-a97c-be8cda6db5eb · outbound

This paper cites Crapo, Chromatic polynomials for a join of graphs.Combinatorial theory and its applications, I–III (Proc.

The Penrose-Kauffman Polynomial Crapo, Chromatic polynomials for a join of graphs.Combinatorial theory and its applications, I–III (Proc

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:17.005451Z

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 f185fe4e-d388-4974-b3ea-b3000dc71529 · outbound

This paper cites Diestel, Graph Theory, 5th ed., Springer-Verlag, Berlin.

The Penrose-Kauffman Polynomial Diestel, Graph Theory, 5th ed., Springer-Verlag, Berlin

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:17.001499Z

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 922cd1bd-e86a-4952-a02b-5555d03d99d8 · outbound

This paper cites an unresolved cited work.

The Penrose-Kauffman Polynomial Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-05-21T15:15:17.003519Z

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 cbe741ca-44e4-44b8-a842-e489589b09c3 · outbound

This paper cites an unresolved cited work.

The Penrose-Kauffman Polynomial Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-05-21T15:15:16.989793Z

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 82795351-5039-41cf-9ca8-6b12de829fda · outbound

This paper cites Jacobson, Basic Algebra I, W.

The Penrose-Kauffman Polynomial Jacobson, Basic Algebra I, W

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:16.997622Z

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 5deabf5d-6904-4acc-8833-59ea3a12a854 · outbound

This paper cites Jaeger, On transition polynomials of 4-regular graphs, In Cycles and rays (Montreal, PQ, 1987), vol.

The Penrose-Kauffman Polynomial Jaeger, On transition polynomials of 4-regular graphs, In Cycles and rays (Montreal, PQ, 1987), vol

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:16.995797Z

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 a99ecc91-76b2-4ef4-90d6-ad849a8205e4 · outbound

This paper cites an unresolved cited work.

The Penrose-Kauffman Polynomial Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-05-21T15:15:16.993766Z

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 abdfffa0-a2b1-4d18-850f-509829019a9f · outbound

This paper cites Kauffman,Colorings and Penrose evaluations, virtual colloquium presented at University of South Alabama, January 18.

The Penrose-Kauffman Polynomial Kauffman,Colorings and Penrose evaluations, virtual colloquium presented at University of South Alabama, January 18

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:16.981020Z

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 84708551-382f-4cda-8502-d383378ea0b3 · outbound

This paper cites Kauffman, Multi-virtual knot theory, J.

The Penrose-Kauffman Polynomial Kauffman, Multi-virtual knot theory, J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:16.991838Z

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 3712ec5f-914b-4466-839c-9d9170f29a60 · outbound

This paper cites Kauffman, New invariants in the theory of knots.

The Penrose-Kauffman Polynomial Kauffman, New invariants in the theory of knots

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:16.999587Z

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 aac5b89e-dcf1-410f-bc08-c2dc7d0f7f8e · outbound

This paper cites Lickorish and M.B.

The Penrose-Kauffman Polynomial Lickorish and M.B

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:16.984926Z

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 f602a988-a230-4baf-ad15-2f88ea348101 · outbound

This paper cites Ellis-Monaghan, I.

The Penrose-Kauffman Polynomial Ellis-Monaghan, I

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:16.978703Z

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 4f7cbdaf-746d-4cb3-8de0-82f5969f8857 · outbound

This paper cites Menasco and M.

The Penrose-Kauffman Polynomial Menasco and M

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:16.976677Z

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 ea6e5f1f-3074-4dab-957d-f32ef7ec6f21 · outbound

This paper cites Penrose,Applications of negative-dimensional tensors, in Combina- torial Mathematics and its Applications (Proc.

The Penrose-Kauffman Polynomial Penrose,Applications of negative-dimensional tensors, in Combina- torial Mathematics and its Applications (Proc

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:16.983047Z

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 e13aefe8-a276-46ff-a482-a006d427e967 · outbound

This paper cites Silver and S.G.

The Penrose-Kauffman Polynomial Silver and S.G

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:16.974396Z

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 4a039887-722b-4b26-b45e-b4d5d5d3e911 · outbound

This paper cites Whitney,2-isomorphic graphs, Amer.

The Penrose-Kauffman Polynomial Whitney,2-isomorphic graphs, Amer

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:15:16.987933Z

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

No inbound Pith citation observations are available.