Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T18:42:17.899886Z
Paper Citation Record · LEDGER
Biquandle Virtual Brackets and Virtual Knotoids
As of 17 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2507.07612.
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 2026-08-17T06:30:58.91139+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 exact2
- verified fuzzy15
- unresolved0
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation d9437d0b-1b88-4bcc-8f73-56c5f87e523b · outbound
This paper cites Knots related by knotoids.
Biquandle Virtual Brackets and Virtual Knotoids Knots related by knotoids
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:21.410436Z
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 7d82bdac-65f5-4764-a165-27729d2bcb81 · outbound
This paper cites A table of virtual links.
Biquandle Virtual Brackets and Virtual Knotoids A table of virtual links
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:21.252908Z
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 40841a59-b72a-46ab-b0b4-20d614992db6 · outbound
This paper cites Thistlethwaite Theorems for Knotoids and Linkoids.
Biquandle Virtual Brackets and Virtual Knotoids Thistlethwaite Theorems for Knotoids and Linkoids
Reference 3
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T18:42:18.369487Z
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 fb74a83c-a660-49a8-a633-c7627481ac96 · outbound
This paper cites Studies of global and local entanglements of individual protein chains using the concept of knotoids.
Biquandle Virtual Brackets and Virtual Knotoids Studies of global and local entanglements of individual protein chains using the concept of knotoids
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:20.951317Z
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 2c73edc1-9bcb-4d1e-8faa-6583c1baae71 · outbound
This paper cites Topological models for open-knotted protein chains using the concepts of knotoids and bonded knotoids.
Biquandle Virtual Brackets and Virtual Knotoids Topological models for open-knotted protein chains using the concepts of knotoids and bonded knotoids
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:20.727070Z
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 fc0c0fbf-7813-4e6f-9dfa-844298ddf194 · outbound
This paper cites Invariants of bonded knotoids and applications to protein folding.
Biquandle Virtual Brackets and Virtual Knotoids Invariants of bonded knotoids and applications to protein folding
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:20.477661Z
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 b8df1aea-a4c5-4613-b586-fb9807f1ba6e · outbound
This paper cites New invariants of knotoids.European Journal of Combinatorics, 65:186–229, 2017.
Biquandle Virtual Brackets and Virtual Knotoids New invariants of knotoids.European Journal of Combinatorics, 65:186–229, 2017
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:20.270911Z
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 78050681-2500-4c19-a69c-12b98a26aec4 · outbound
This paper cites Parity, virtual closure and minimality of knotoids.
Biquandle Virtual Brackets and Virtual Knotoids Parity, virtual closure and minimality of knotoids
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:20.019761Z
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 c2bf1951-a9fb-4718-b0f0-cec4f80997ed · outbound
This paper cites Quantum invariants of knotoids.Communications in Mathematical Physics , 387(3):1681–1728, 2021.
Biquandle Virtual Brackets and Virtual Knotoids Quantum invariants of knotoids.Communications in Mathematical Physics , 387(3):1681–1728, 2021
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:19.818015Z
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 a5592e71-e7db-4c9d-9143-03256423f4a0 · outbound
This paper cites Virtual knotoids in thickened surfaces.arXiv preprint arXiv:2502.18160, 2025.
Biquandle Virtual Brackets and Virtual Knotoids Virtual knotoids in thickened surfaces.arXiv preprint arXiv:2502.18160, 2025
Reference 10
- Resolution
- verified exact
- raw_fallback, observed 2026-08-06T18:42:18.203686Z
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 7f59c583-ea6e-4434-aaed-a4d9b9484553 · outbound
This paper cites Biquandle coloring invariants of knotoids.
Biquandle Virtual Brackets and Virtual Knotoids Biquandle coloring invariants of knotoids
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:19.595736Z
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 89adee69-9e7e-45d0-8a74-deaf5e06e93b · outbound
This paper cites Biquandle brackets and knotoids.
Biquandle Virtual Brackets and Virtual Knotoids Biquandle brackets and knotoids
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:19.404740Z
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 aeefc824-5701-48df-af29-aa91f6639564 · outbound
This paper cites Introduction to virtual knot theory.
Biquandle Virtual Brackets and Virtual Knotoids Introduction to virtual knot theory
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:19.228644Z
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 f5c0e063-aa6e-4b5b-a57f-c0d76d3e3d7f · outbound
This paper cites Framed knotoids and their quantum invariants.
Biquandle Virtual Brackets and Virtual Knotoids Framed knotoids and their quantum invariants
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:19.011892Z
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 20110630-1488-4265-bf35-54d07dc2020b · outbound
This paper cites Quantum enhancements and biquandle brackets.
Biquandle Virtual Brackets and Virtual Knotoids Quantum enhancements and biquandle brackets
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:18.796637Z
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 e7b18ab2-34d4-4f01-a613-d91f0188e204 · outbound
This paper cites Biquandle virtual brackets.
Biquandle Virtual Brackets and Virtual Knotoids Biquandle virtual brackets
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:18.644747Z
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 e26194b4-9712-45c7-853d-a2f392770e5f · outbound
This paper cites Knotoids.
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T18:42:18.485742Z
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.