Paper Citation Record · LEDGER

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots

As of 16 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2608.03818.

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

pith.paper-citation-record.v1
2608.03818 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T11:59:40.394090Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

24 of 24 outbound references displayed

verified exact17
verified fuzzy1
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation dce32874-d036-46f4-9fd9-b26b48a4d27d · outbound

This paper cites Di Prisa, D.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots Di Prisa, D

Reference 1

Resolution: verified exact; raw_fallback, observed 2026-08-05T11:59:40.867423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e45fb6a7-5eef-4263-bb50-8fd51777073c · outbound

This paper cites an unresolved cited work.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-05T11:59:39.867414Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3cb1a149-a3ee-481e-9e06-6f4cc098ed7c · outbound

This paper cites Kasprowski, 4 -Manifolds with a Given Boundary, preprint, 2025, arXiv:2510.18836, https://arxiv.org/abs/2510.18836.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots Kasprowski, 4 -Manifolds with a Given Boundary, preprint, 2025, arXiv:2510.18836, https://arxiv.org/abs/2510.18836

Reference 3

Resolution: verified exact; raw_fallback, observed 2026-08-05T11:59:40.788284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 773a608c-1b91-4a41-92ed-1bcc9c297f84 · outbound

This paper cites H., The Derived Module of a Homomorphism, Advances in Mathematics, vol.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots H., The Derived Module of a Homomorphism, Advances in Mathematics, vol

Reference 4

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.572846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 225f9e47-9e6e-41a6-b1ce-fb0febf0cdfd · outbound

This paper cites Rourke, Racks and Links in Codimension Two, Journal of Knot Theory and Its Ramifications, vol.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots Rourke, Racks and Links in Codimension Two, Journal of Knot Theory and Its Ramifications, vol

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-05T11:59:40.216038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4735694f-1cd4-4e83-9e62-23ba8792cf1d · outbound

This paper cites McA., Twist-Spun Torus Knots, Proceedings of the American Mathematical Society, vol.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots McA., Twist-Spun Torus Knots, Proceedings of the American Mathematical Society, vol

Reference 6

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.555087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8e74f466-7df9-4bd8-9317-251aa443cf01 · outbound

This paper cites On biquandle-based invariant of immersed surface-links, Yoshikawa oriented fifth move, and ribbon 2-knots.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots On biquandle-based invariant of immersed surface-links, Yoshikawa oriented fifth move, and ribbon 2-knots

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-05T11:59:40.335599Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 994b95e7-c6a3-4e3f-a691-25ae9e92549c · outbound

This paper cites an unresolved cited work.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-05T11:59:40.339931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9da73a8a-8062-4429-a0e4-3c685e935bee · outbound

This paper cites an unresolved cited work.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots Unresolved cited work

Reference 9

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.536799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 10efc2c6-ede7-4cd9-ab3e-9b2da0139c77 · outbound

This paper cites J., Jr., The Homotopy Groups of Knots I.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots J., Jr., The Homotopy Groups of Knots I

Reference 10

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.526041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c8ceeef0-f440-4c3d-af62-886c650a6a44 · outbound

This paper cites V., Distributive Groupoids in Knot Theory, Matematicheskii Sbornik, vol.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots V., Distributive Groupoids in Knot Theory, Matematicheskii Sbornik, vol

Reference 11

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.515713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c5b3a55e-4637-47d6-ba95-fddbc6fa0307 · outbound

This paper cites an unresolved cited work.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:59:40.891926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 09eea160-77d3-4d1a-b2f5-b75c63110dc7 · outbound

This paper cites D., and F.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots D., and F

Reference 13

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.505481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6e40c948-013d-4167-b80c-eae9b416f83b · outbound

This paper cites P., The Homotopy Type of Four-Dimensional Knot Complements, Mathematische Zeitschrift, vol.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots P., The Homotopy Type of Four-Dimensional Knot Complements, Mathematische Zeitschrift, vol

Reference 14

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.495553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b996f264-7166-4258-9f5a-220f905451f3 · outbound

This paper cites P., and A.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots P., and A

Reference 15

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.485533Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a6454ee6-9dbe-4e9b-82b6-ed5b8b59abee · outbound

This paper cites Tanaka, The Knot Quandles of Suciu's Ribbon n -Knots and Automorphisms on the Free Group of Rank Two, Bulletin of the Australian Mathematical Society, vol.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots Tanaka, The Knot Quandles of Suciu's Ribbon n -Knots and Automorphisms on the Free Group of Rank Two, Bulletin of the Australian Mathematical Society, vol

Reference 16

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.474058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8ae7493c-0433-4349-9b09-beff2100964a · outbound

This paper cites I., Homotopy Type Invariants of Four-Dimensional Knot Complements, Ph.D.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots I., Homotopy Type Invariants of Four-Dimensional Knot Complements, Ph.D

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:59:40.878708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 845c8d8a-578f-429a-9701-cd3b6a1258b0 · outbound

This paper cites I., Infinitely Many Ribbon Knots with the Same Fundamental Group, Mathematical Proceedings of the Cambridge Philosophical Society, vol.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots I., Infinitely Many Ribbon Knots with the Same Fundamental Group, Mathematical Proceedings of the Cambridge Philosophical Society, vol

Reference 18

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.463781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation cf4d837a-dee8-46f0-b80f-ab39edcb6bb0 · outbound

This paper cites an unresolved cited work.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots Unresolved cited work

Reference 19

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.450569Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 109b28c8-c5f5-4d2f-a159-09a2a4884e80 · outbound

This paper cites Taniguchi, 2 -Knots with the Same Knot Group but Different Knot Quandles, Journal of the Mathematical Society of Japan, vol.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots Taniguchi, 2 -Knots with the Same Knot Group but Different Knot Quandles, Journal of the Mathematical Society of Japan, vol

Reference 20

Resolution: verified exact; raw_fallback, observed 2026-08-05T11:59:40.689889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fa06fd70-a53a-4dfd-9ae2-06a387b6b516 · outbound

This paper cites The Medial Quandle of a Link, Journal of Knot Theory and Its Ramifications, vol.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots The Medial Quandle of a Link, Journal of Knot Theory and Its Ramifications, vol

Reference 21

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.439794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8ed434d0-729a-4167-ada0-02a2a87b0e19 · outbound

This paper cites The quandle and group for higher-dimensional and virtual knots.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots The quandle and group for higher-dimensional and virtual knots

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-05T11:59:40.605273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b0a4f7bb-6c73-4700-8789-7f2be7fc58ea · outbound

This paper cites Knot quandles distinguish Suciu's ribbon knots.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots Knot quandles distinguish Suciu's ribbon knots

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-05T11:59:40.390678Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eed4ab14-26bc-4eee-86c4-63175d77c470 · outbound

This paper cites C., Twisting Spun Knots, Transactions of the American Mathematical Society, vol.

Fundamental Quandles Do Not Determine the First Postnikov Invariant of 2-Knots C., Twisting Spun Knots, Transactions of the American Mathematical Society, vol

Reference 24

Resolution: verified exact; doi, observed 2026-08-05T11:59:40.427231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

No inbound Pith citation observations are available.