Pith. sign in

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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.696509Z digest=sha256:3ca291476ed4a172fcc076a46d86034f6597eb675b5670b12b39ef82e76437d7

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.707228Z digest=sha256:a996973cd16fba8800a5fbb308d9149459c4f553962ea81028d0ac8745bc9f86

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.712113Z digest=sha256:1f76588d257dd8bf52a9f13b26cf7fc20d9db757e45fe72815833c582880fa6a

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.717260Z digest=sha256:13070b7316891c11669f6a05edefe3c8fbaf63a7b6daab73eec9aeea84c33e96

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.722414Z digest=sha256:5d225e6423e2168291137bdb68d4c2561806015df999dc48477f97ac347af154

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.727817Z digest=sha256:80ec870beba152dd2148b12917585acc771e4c6489b91aa0d7fed7bb40239559

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.732692Z digest=sha256:7b1ea6286e107f24418f81cc53f14d0483d99ac3ab91aef25b9320df955bcd68

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.737518Z digest=sha256:e9d24608f4389e3c284edf6738306c9a17033b81e5bb9358cfc1a8bc1e3a7b85

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.742159Z digest=sha256:25a41e45d7d580030d5679a1743521ee0733bee4d037c5e7b8243e68dc8cfdcd

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.746817Z digest=sha256:f443f53f00f3a0ca3945563b8cac1c9ffd0398ececd9b81c812c896120a6bfcc

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.751798Z digest=sha256:85a76860fed4f9cc39d30aa596cad6cb9ee82f7a5c80795454c073a06ecfbb35

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.756805Z digest=sha256:1f8a8c0fa23c73b2e1f72d50b7bf173427495b8fcd2b4fb7c1a560ffdb32dbfb

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.765815Z digest=sha256:8a75a13598e98450894adefe2c65a7ec2835be0617e0fb1d99dbc07cdb8b1f53

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.776043Z digest=sha256:8e4e073f0b13dd5bc4133fdb02f61625a1aad9cd1972745665d7997aedce5de9

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:e8ffa0def2b2a5417cd8c5ed2abf3b84c3f819bf04b66dc1064de8674e2d4054

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=sha256:666d44a39530f8ce28b76cc851ea542b7c0a25d52ef625b990db3685b148f357

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.812031Z digest=sha256:4ab16b2cb55c970ebf1baa0ee22a497c43dcdce351bdc095e430a0e5e986bded

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

Resolution
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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T23:48:55.817634Z digest=sha256:c49fe86d39fb97bbd33aac45b7d9062b44c9480b50a08c0dd282ab5e66644921

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

Resolution
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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-07T12:58:11.117306Z digest=sha256:86da0dc748b2f6f6e668ea3787b36d0f15fd9e43bd3fe690106db46b9351827d