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Paper Citation Record · LEDGER

Characterizations of knot groups and knot symmetric quandles of surface-links

As of 16 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 1 inbound Pith citation observation for arXiv:2412.20081.

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

pith.paper-citation-record.v1
2412.20081 v2

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:48:55.817634Z

measured 26 of 26 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:58:11.117306Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T12:58:15.778990Z

Reference resolution

25 of 25 outbound references displayed

  • verified exact0
  • verified fuzzy13
  • unresolved12
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d2212d0f-7df5-4ae4-8a40-2fc6e7b3f798 · outbound

This paper cites Alexander.

Characterizations of knot groups and knot symmetric quandles of surface-links Alexander

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:56.221467Z

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.

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Observation 2c9c59d5-a7b3-40b5-b658-e4bcd6a1a720 · outbound

This paper cites Theorie der Z ¨opfe.

Characterizations of knot groups and knot symmetric quandles of surface-links Theorie der Z ¨opfe

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-10T23:48:55.702285Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:48:55.702285Z digest=sha256:9f4b936c2edb41b0cfebf05eeef35caa57af8c76bea5e8cfe54fd2fc8d20471c

Observation 8ff026bb-f2d1-472e-a971-fac2d3777e2a · outbound

This paper cites Configuration spaces of rings and wickets.

Characterizations of knot groups and knot symmetric quandles of surface-links Configuration spaces of rings and wickets

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:56.193177Z

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.

source=pdf_text observed=2026-08-10T23:48:55.707228Z digest=sha256:e48047dac4cdc87145f5ca4f2d9e64b9010de6b1bad0d1de4f0488f9010d92c2

Observation 97af69bc-1a13-4918-9980-d599bd268b21 · outbound

This paper cites Dhanwani, Hitesh Raundal, and Mahender Singh.

Characterizations of knot groups and knot symmetric quandles of surface-links Dhanwani, Hitesh Raundal, and Mahender Singh

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:56.177715Z

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.

source=pdf_text observed=2026-08-10T23:48:55.712113Z digest=sha256:b6244666b0bec2d621a25852fc52cb29b16d4fa098449ba3757cb56825e95f5e

Observation 2c17cb34-f7d6-49d4-9fac-42703767f6af · outbound

This paper cites Racks and links in codimension two.

Characterizations of knot groups and knot symmetric quandles of surface-links Racks and links in codimension two

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:56.161890Z

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.

source=pdf_text observed=2026-08-10T23:48:55.717260Z digest=sha256:665695b4f39d80f26fafb0fffa8056cba5b8a8370ed2e61a924834556b1160bc

Observation d11b9e7f-809f-4a56-96a9-159a823956aa · outbound

This paper cites Gonz ´alez-Acu˜na.

Characterizations of knot groups and knot symmetric quandles of surface-links Gonz ´alez-Acu˜na

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:56.146099Z

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.

source=pdf_text observed=2026-08-10T23:48:55.722414Z digest=sha256:734adf6c249fd89ea69f442da38e9327fbb8a03352efa47a74c0416cfdc84d50

Observation 9147df5b-f1d4-4e39-b538-fc492c2eae4f · outbound

This paper cites On the knot quandle of a fibered knot, finiteness and equivalence of knot quandles.

Characterizations of knot groups and knot symmetric quandles of surface-links On the knot quandle of a fibered knot, finiteness and equivalence of knot quandles

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:56.128878Z

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.

source=pdf_text observed=2026-08-10T23:48:55.727817Z digest=sha256:10fdff516cc915ffb38aee158d24a1f1b409dca4b614b85ea418e009fb44befc

Observation aafe45ea-5d47-4aa7-a6e3-f2ec7a177558 · outbound

This paper cites an unresolved cited work.

Characterizations of knot groups and knot symmetric quandles of surface-links Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:48:56.112299Z

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.

source=pdf_text observed=2026-08-10T23:48:55.732692Z digest=sha256:991bc45babc722a3fa464fe914b198c6a4bd007494a64e2d2d128d64caada8d6

Observation 1acbd37e-6e00-415d-9419-f157fddbca6d · outbound

This paper cites Non-orientable surfaces in 4-space.

Characterizations of knot groups and knot symmetric quandles of surface-links Non-orientable surfaces in 4-space

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:56.093334Z

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.

source=pdf_text observed=2026-08-10T23:48:55.737518Z digest=sha256:82ef080ee641481e87a38533a6fa093d076f5634211edde2b14936e59fdf6114

Observation 5290cb64-7958-43f3-8c8d-3310438a622b · outbound

This paper cites A characterization of groups of closed orientable surfaces in 4-space.

Characterizations of knot groups and knot symmetric quandles of surface-links A characterization of groups of closed orientable surfaces in 4-space

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:56.077326Z

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.

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Observation e1d2ce38-af3c-49c4-b66d-1429b3edad2e · outbound

This paper cites On braid monodromies of non-simple braided surfaces.

Characterizations of knot groups and knot symmetric quandles of surface-links On braid monodromies of non-simple braided surfaces

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:56.060129Z

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.

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Observation 2856a1bd-ff98-47e9-a353-6ae4b36ce116 · outbound

This paper cites Quandles with good involutions, their homologies and knot invariants.

Characterizations of knot groups and knot symmetric quandles of surface-links Quandles with good involutions, their homologies and knot invariants

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:56.042754Z

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.

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Observation 5ce01c87-fb1b-4819-8ad4-409ef6d0f1c6 · outbound

This paper cites Quandles and symmetric quandles for higher dimensional knots.

Characterizations of knot groups and knot symmetric quandles of surface-links Quandles and symmetric quandles for higher dimensional knots

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:56.025706Z

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.

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Observation 5e5bd0de-5a1d-4742-9e89-862edbe881c5 · outbound

This paper cites Surface-Knots in 4-Space.

Characterizations of knot groups and knot symmetric quandles of surface-links Surface-Knots in 4-Space

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-10T23:48:55.761188Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:48:55.761188Z digest=sha256:28c5fc08b03e491a51b948a6710a7b64610e8c5f9a8f40ba4a272c3601ef3a3e

Observation d462a6a2-24f6-4cf6-b6fc-a67ce6acac6d · outbound

This paper cites Homology groups of symmetric quandles and cocycle invariants of links and surface-links.Trans.

Characterizations of knot groups and knot symmetric quandles of surface-links Homology groups of symmetric quandles and cocycle invariants of links and surface-links.Trans

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:55.995653Z

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.

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Observation 5ebf1f34-ae00-4c31-93a9-c8cccd350af0 · outbound

This paper cites On the Alexander polynomials of 2-spheres in a 4-sphere.

Characterizations of knot groups and knot symmetric quandles of surface-links On the Alexander polynomials of 2-spheres in a 4-sphere

Reference 16

Resolution
unresolved
no resolver link, observed 2026-08-10T23:48:55.771119Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:48:55.771119Z digest=sha256:762754a5276a646ec16b21b5569aecef1e1e6c32535a21435b68143be78fd030

Observation 546f5bf5-808c-490a-af93-4f37e960f79c · outbound

This paper cites an unresolved cited work.

Characterizations of knot groups and knot symmetric quandles of surface-links Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:48:55.965754Z

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.

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Observation 30704aa8-679a-4e15-83a3-c1fe74a680e0 · outbound

This paper cites Quandles versus symmetric quandles for oriented links.

Characterizations of knot groups and knot symmetric quandles of surface-links Quandles versus symmetric quandles for oriented links

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-10T23:48:55.780918Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:48:55.780918Z digest=sha256:f78c98a7ab6c6189aa8926e760a8ddc4901303bfa2316eeef53225950d3b81f5

Observation 81d8c921-1246-41e3-8861-b6f769f8b91f · outbound

This paper cites Braided surfaces and Seifert ribbons for closed braids.

Characterizations of knot groups and knot symmetric quandles of surface-links Braided surfaces and Seifert ribbons for closed braids

Reference 19

Resolution
unresolved
no resolver link, observed 2026-08-10T23:48:55.786658Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:48:55.786658Z digest=sha256:f60fe4f47a06bd6afb15af8e8d1a550a36ee71975439c637db9a948b96917265

Observation addb6b37-62a1-47d9-81d3-af9eb54bab0d · outbound

This paper cites $2$-knots with the same knot group but different knot quandles.

Characterizations of knot groups and knot symmetric quandles of surface-links $2$-knots with the same knot group but different knot quandles

Reference 20

Resolution
unresolved
no resolver link, observed 2026-08-10T23:48:55.791613Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:48:55.791613Z digest=sha256:4efbef9b4dd7048e5f25c235139d6fc52b032a1bd93f0eae2cd8e8fed2737dda

Observation 64892256-0fb0-4a29-9119-bbc8191d3080 · outbound

This paper cites an unresolved cited work.

Characterizations of knot groups and knot symmetric quandles of surface-links Unresolved cited work

Reference 21

Resolution
unresolved
no resolver link, observed 2026-08-10T23:48:55.797083Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:48:55.797083Z digest=sha256:9e47ab07713ee068ec53d0cb57a55fdbbb70b64808e890345aa96745442f7fcc

Observation 92342645-d157-46f6-842b-42d57792cbf3 · outbound

This paper cites A plat form presentation for surface-links.

Characterizations of knot groups and knot symmetric quandles of surface-links A plat form presentation for surface-links

Reference 22

Resolution
unresolved
no resolver link, observed 2026-08-10T23:48:55.801991Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:48:55.801991Z digest=sha256:f7c36f1e959bd199509a78426dfa0c012c7f032012177f0fc5ea5151d397f5a0

Observation d937ed6c-f157-4298-9208-6838281a4589 · outbound

This paper cites Computation of the knot symmetric quandle and its application to the plat index of surface-links.

Characterizations of knot groups and knot symmetric quandles of surface-links Computation of the knot symmetric quandle and its application to the plat index of surface-links

Reference 23

Resolution
unresolved
no resolver link, observed 2026-08-10T23:48:55.806909Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:48:55.806909Z digest=sha256:577659f8127a82a313fa9ff2739700555f33c1984defa62792f543a146cdc401

Observation 95d12ea4-c181-46b6-ad5e-fefebc5f01dd · outbound

This paper cites An enumeration of surfaces in four-space.

Characterizations of knot groups and knot symmetric quandles of surface-links An enumeration of surfaces in four-space

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:48:55.905835Z

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.

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Observation 89ea36d9-5978-48ee-8ba6-c6da6a39df72 · outbound

This paper cites an unresolved cited work.

Characterizations of knot groups and knot symmetric quandles of surface-links Unresolved cited work

Reference 25

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unresolved
raw_fallback, observed 2026-08-10T23:48:55.888512Z

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.

source=pdf_text observed=2026-08-10T23:48:55.817634Z digest=sha256:8c4e42e6c5957b220c019a3c077d8a107a1b0e77ca09cd86e2dd8a1cfdb55bb7

Pith citing papers

Observation e34aebdb-a5ca-4ff1-86ea-8fa35b12fb25 · inbound

Associated groups of symmetric quandles cites this paper.

Associated groups of symmetric quandles Characterizations of knot groups and knot symmetric quandles of surface-links

Reference 57

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verified exact
local_arxiv, observed 2026-08-07T12:58:15.850011Z

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.

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