Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T17:57:19.191165Z
Paper Citation Record · LEDGER
Biquandle cocycle condition for invariants of immersed surface-links in the four-space
As of 16 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.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.