Paper Citation Record · LEDGER

New relations for the Penrose polynomial

As of 11 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2606.06643.

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

pith.paper-citation-record.v1
2606.06643 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-28T00:15:15.650075Z

measured 22 of 22 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 2026-08-01T07:05:34.601623Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

21 of 21 outbound references displayed

verified exact5
verified fuzzy0
unresolved14
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e92f5984-1d0e-41e4-8614-76835ff5f6c2 · outbound

This paper cites Aigner, The Penrose polynomial of a plane graph , Mathematische Annalen, 307, 173-189, 1997.

New relations for the Penrose polynomial Aigner, The Penrose polynomial of a plane graph , Mathematische Annalen, 307, 173-189, 1997

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 99bf1435-0f53-44c4-9bd4-627f4345823c · outbound

This paper cites A Cohomology Theory for Planar Trivalent Graphs with Perfect Matchings.

New relations for the Penrose polynomial A Cohomology Theory for Planar Trivalent Graphs with Perfect Matchings

Reference 2

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T14:37:04.193941Z

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 a7f2cfcb-d469-49c5-95e6-5ed9c490a5be · outbound

This paper cites Baldridge, L.

New relations for the Penrose polynomial Baldridge, L

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-06-28T00:21:28.390945Z

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 9df54d74-09f4-4159-a266-da33b68b3a9a · outbound

This paper cites Baldridge, A.

New relations for the Penrose polynomial Baldridge, A

Reference 4

Resolution: malformed identifier; doi_truncated, observed 2026-06-28T00:21:28.392645Z

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 517b8b08-f50f-4b75-835c-f771fa3cd591 · outbound

This paper cites A topological quantum field theory approach to graph coloring.

New relations for the Penrose polynomial A topological quantum field theory approach to graph coloring

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-07-02T14:37:04.191152Z

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 b829ab51-822e-41a2-b678-aae82d7c1aa3 · outbound

This paper cites A new way to prove configuration reducibility using gauge theory.

New relations for the Penrose polynomial A new way to prove configuration reducibility using gauge theory

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-07-02T14:37:04.196715Z

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 c8375be8-c28c-4050-8dc2-c9b8bfbe8500 · outbound

This paper cites Baldridge, L.

New relations for the Penrose polynomial Baldridge, L

Reference 7

Resolution: verified exact; doi, observed 2026-06-28T00:21:28.388456Z

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 4dce9a66-9432-41e3-9d0e-d74004c6f5ef · outbound

This paper cites an unresolved cited work.

New relations for the Penrose polynomial Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d531f840-31f7-4d4f-98a4-3103ce357f7b · outbound

This paper cites an unresolved cited work.

New relations for the Penrose polynomial Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation be14ce4b-c815-4e7d-a94a-543c004aaa7f · outbound

This paper cites Snarks, boojums, and other conjectures related to the four-color-map theorem.

New relations for the Penrose polynomial Snarks, boojums, and other conjectures related to the four-color-map theorem

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9dc6f160-1bd0-4738-8a21-3b8c307118f4 · outbound

This paper cites American Mathematical Monthly , vol.

New relations for the Penrose polynomial American Mathematical Monthly , vol

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 583d2b18-7c05-4f42-993c-9e0a778976a4 · outbound

This paper cites an unresolved cited work.

New relations for the Penrose polynomial Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation afc14d5d-48e8-4ae0-8245-81e9805cf37f · outbound

This paper cites an unresolved cited work.

New relations for the Penrose polynomial Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5c385775-854e-4f0f-9c67-979da85f9d78 · outbound

This paper cites an unresolved cited work.

New relations for the Penrose polynomial Unresolved cited work

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-07-02T14:37:04.188548Z

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 809dde97-37fa-4454-bb4e-2f133aa31780 · outbound

This paper cites Khovanov, A categorification of the Jones polynomial, Duke Math.

New relations for the Penrose polynomial Khovanov, A categorification of the Jones polynomial, Duke Math

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f96eab20-e729-4bb7-9f5a-80e40bbbf810 · outbound

This paper cites Lee, An endomorphism of the Khovanov invariant, Adv.

New relations for the Penrose polynomial Lee, An endomorphism of the Khovanov invariant, Adv

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1fb90e74-717a-47c8-a75f-41639b98f2c6 · outbound

This paper cites Thesis, Grenoble 1977.

New relations for the Penrose polynomial Thesis, Grenoble 1977

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dafd3ea4-b7ec-4cb9-87a4-9d7e22f69f5f · outbound

This paper cites Penrose, ``Applications of negative dimensional tensors,'' in Combinatorial Mathematics and Its Applications , Academic Press (1971).

New relations for the Penrose polynomial Penrose, ``Applications of negative dimensional tensors,'' in Combinatorial Mathematics and Its Applications , Academic Press (1971)

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10b17a4c-1edf-4c7d-a62c-002b42753c52 · outbound

This paper cites Sur le th\'eor\`me de Tait.

New relations for the Penrose polynomial Sur le th\'eor\`me de Tait

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47799d97-77f9-4a58-b72b-9de750b14a26 · outbound

This paper cites Combin.TheorySer.B 70 (1997),no.1, 166-183.

New relations for the Penrose polynomial Combin.TheorySer.B 70 (1997),no.1, 166-183

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22567112-6ed1-4370-828c-5aed01e93d68 · outbound

This paper cites T., On the algebraic theory of graph colorings , J.

New relations for the Penrose polynomial T., On the algebraic theory of graph colorings , J

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-28T00:15:15.650075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 35f0bd7b-39d8-439f-b19f-d183c841e05a · inbound

New relations for the vertex polynomial cites this paper.

New relations for the vertex polynomial New relations for the Penrose polynomial

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T07:05:34.601623Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.