Paper Citation Record · LEDGER

Biquandle cocycle condition for invariants of immersed surface-links in the four-space

As of 17 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2507.20360.

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

pith.paper-citation-record.v1
2507.20360 v2

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T17:57:19.191165Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

17 of 17 outbound references displayed

verified exact0
verified fuzzy15
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 69956e67-95e9-4398-aa66-67ea88f2a062 · outbound

This paper cites Audoux, J.B.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Audoux, J.B

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.533642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 92599173-0acb-495c-889b-2e82e656242b · outbound

This paper cites Carrell, The surface biquandle, Pomona College, 2009.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Carrell, The surface biquandle, Pomona College, 2009

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.517372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 21ef74e6-fec9-4f15-bcca-bbad9ac157ec · outbound

This paper cites Carter, M.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Carter, M

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.491254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9f6a005e-1e2b-4adc-afc6-862091cf4039 · outbound

This paper cites Carter, S.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Carter, S

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.475272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0488d4c3-a3ec-4e1f-b037-0cba944790bf · outbound

This paper cites Carter and M.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Carter and M

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.453200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8cbf8c1b-10ef-4d87-a097-62a91857c6c6 · outbound

This paper cites Jab onowski, Knotted surfaces and equivalencies of their diagrams without triple points, J.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Jab onowski, Knotted surfaces and equivalencies of their diagrams without triple points, J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.435763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 98848953-f01b-41f5-948b-f8ec2ea0e383 · outbound

This paper cites Jab onowski, Minimal generating sets of moves for surfaces immersed in the four-space, J.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Jab onowski, Minimal generating sets of moves for surfaces immersed in the four-space, J

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.417769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f6643813-13b4-4fec-83e7-635007778c3a · outbound

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

Biquandle cocycle condition for invariants of immersed surface-links in the four-space On biquandle-based invariant of immersed surface-links, Yoshikawa oriented fifth move, and ribbon 2-knots

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T17:57:19.145876Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5353a99b-a893-42df-8f62-8dec05bb6230 · outbound

This paper cites Kamada, Surface-Knots in 4 -Space, Springer Monographs in Mathematics, Springer (2017).

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Kamada, Surface-Knots in 4 -Space, Springer Monographs in Mathematics, Springer (2017)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.401097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 04151e35-ae2b-4a80-a070-3c08bb499c7d · outbound

This paper cites Kamada, A.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Kamada, A

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.384985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 938aa874-8fb2-405d-87a2-4e3f6cc52be5 · outbound

This paper cites Kauffman and D.E.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Kauffman and D.E

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.367794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ff1af081-1f00-48b5-a773-4d880045c646 · outbound

This paper cites Kawamura, On relationship between seven types of Roseman moves, accepted by Topology and its Applications 2015.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Kawamura, On relationship between seven types of Roseman moves, accepted by Topology and its Applications 2015

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.349752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b4c34109-0148-4821-9890-a236902ae66e · outbound

This paper cites Nuno-Ballesteros and O.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Nuno-Ballesteros and O

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.330355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 576e6317-b100-45f5-9691-d631433a8056 · outbound

This paper cites Roseman, Reidemeister-type moves for surfaces in four-dimensional space, in Knot Theory, Banach Center Publications 42 (1998), 347--380.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Roseman, Reidemeister-type moves for surfaces in four-dimensional space, in Knot Theory, Banach Center Publications 42 (1998), 347--380

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.313807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 5a6ae933-b97e-43b2-b20b-84f3d498eec4 · outbound

This paper cites an unresolved cited work.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T17:57:19.291900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 42729fa7-05ab-4687-a52b-ecf7e9436a18 · outbound

This paper cites Satoh, Double decker sets of generic surfaces in 3-space as homology classes, Illinois J.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Satoh, Double decker sets of generic surfaces in 3-space as homology classes, Illinois J

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.269961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 04673286-ddb3-40fb-bbb2-7aed758dfad7 · outbound

This paper cites Yashiro, A note on Roseman moves, Kobe J.

Biquandle cocycle condition for invariants of immersed surface-links in the four-space Yashiro, A note on Roseman moves, Kobe J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T17:57:19.253066Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

No inbound Pith citation observations are available.