Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T14:16:05.136893Z
Paper Citation Record · LEDGER
Thistlethwaite Theorems for Knotoids and Linkoids
As of 17 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 1 inbound Pith citation observation for arXiv:2412.12357.
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, observed 2026-08-06T18:42:16.651848Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-06T18:42:18.342493Z
Reference resolution
26 of 26 outbound references displayed
- verified exact1
- verified fuzzy24
- unresolved1
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation f6c948fe-d502-4b03-8dc6-619e47646c8a · outbound
This paper cites Double branched covers of knotoids.
Thistlethwaite Theorems for Knotoids and Linkoids Double branched covers of knotoids
Reference 1
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T14:16:05.204914Z
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 012a34a7-901d-4ec3-8bf8-2dda12d804d7 · outbound
This paper cites Twisted link theory.
Thistlethwaite Theorems for Knotoids and Linkoids Twisted link theory
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.603618Z
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 ca94437a-3fa1-4b7c-9e2d-8dc97b9e44c2 · outbound
This paper cites Arrow ribbon graphs.
Thistlethwaite Theorems for Knotoids and Linkoids Arrow ribbon graphs
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.587203Z
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 d815422c-0ba2-4ad2-9270-dce4c9d09bdc · outbound
This paper cites Generalized duality for graphs on surfaces and the signed Bollob´ as- Riordan polynomial.
Thistlethwaite Theorems for Knotoids and Linkoids Generalized duality for graphs on surfaces and the signed Bollob´ as- Riordan polynomial
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.571056Z
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 1b76dad4-543a-43fe-a98d-f7ea36717059 · outbound
This paper cites The Kauffman bracket of virtual links and the Bol- lob´ as-Riordan polynomial.Moscow Mathematical Journal , 7(3):409–418, 2007.
Thistlethwaite Theorems for Knotoids and Linkoids The Kauffman bracket of virtual links and the Bol- lob´ as-Riordan polynomial.Moscow Mathematical Journal , 7(3):409–418, 2007
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.554877Z
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 d98814c3-199f-47e3-880c-3982d64ccb2a · outbound
This paper cites Thistlethwaite’s theorem for virtual links.Journal of Knot Theory and Its Ramifications , 17(10):1189 ¨O–1198, 2008.
Thistlethwaite Theorems for Knotoids and Linkoids Thistlethwaite’s theorem for virtual links.Journal of Knot Theory and Its Ramifications , 17(10):1189 ¨O–1198, 2008
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.538633Z
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 6c155119-a162-451f-8cb0-4de220b07962 · outbound
This paper cites The Jones polynomial and graphs on surfaces.
Thistlethwaite Theorems for Knotoids and Linkoids The Jones polynomial and graphs on surfaces
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.522575Z
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 77b6cf62-1435-488d-b839-a43ef2fcc4ef · outbound
This paper cites One conjecture on cut points of virtual links and the arrow polyno- mial of twisted links.
Thistlethwaite Theorems for Knotoids and Linkoids One conjecture on cut points of virtual links and the arrow polyno- mial of twisted links
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.506370Z
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 3f513adc-95b1-4b03-ab8f-7738f31ee05f · outbound
This paper cites Knoto- ID: a tool to study the entanglement of open protein chains using the concept of knotoids.
Thistlethwaite Theorems for Knotoids and Linkoids Knoto- ID: a tool to study the entanglement of open protein chains using the concept of knotoids
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.489945Z
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 5cfedd9a-6f52-424f-85e1-24dc05e72feb · outbound
This paper cites Graphs on surfaces: dualities, polyno- mials, and knots , volume 84.
Thistlethwaite Theorems for Knotoids and Linkoids Graphs on surfaces: dualities, polyno- mials, and knots , volume 84
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.472761Z
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 77942775-9dd4-4790-ab81-87ed7559dce9 · outbound
This paper cites Invariants of multi-linkoids.Mediter- ranean Journal of Mathematics , 20(3):165, 2023.
Thistlethwaite Theorems for Knotoids and Linkoids Invariants of multi-linkoids.Mediter- ranean Journal of Mathematics , 20(3):165, 2023
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.455966Z
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 7af5a176-90b9-4611-a26e-4e9959aa60ea · outbound
This paper cites A systematic classification of knotoids on the plane and on the sphere.
Thistlethwaite Theorems for Knotoids and Linkoids A systematic classification of knotoids on the plane and on the sphere
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T14:16:05.064365Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6c3df063-3bd5-431d-8b86-f9d0c8c65d69 · outbound
This paper cites Knotoids and protein structure.
Thistlethwaite Theorems for Knotoids and Linkoids Knotoids and protein structure
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.439796Z
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 0ab52117-a72d-4445-ab54-ce9548c035ba · outbound
This paper cites Topological models for open-knotted protein chains using the concepts of knotoids and bonded knotoids.
Thistlethwaite Theorems for Knotoids and Linkoids Topological models for open-knotted protein chains using the concepts of knotoids and bonded knotoids
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.423635Z
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 058901bd-ec8e-4a12-84a6-cdbf95ee906d · outbound
This paper cites New invariants of knotoids.European Journal of Combinatorics , 65:186–229, 2017.
Thistlethwaite Theorems for Knotoids and Linkoids New invariants of knotoids.European Journal of Combinatorics , 65:186–229, 2017
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.407103Z
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 3f128ddc-1c9d-4f94-9f0b-c68decc80ad2 · outbound
This paper cites On combinatorial isotopy.
Thistlethwaite Theorems for Knotoids and Linkoids On combinatorial isotopy
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.390899Z
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 012508ce-9fb0-48cb-b7d0-c1fbaebf7afa · outbound
This paper cites State models and the Jones polynomial.
Thistlethwaite Theorems for Knotoids and Linkoids State models and the Jones polynomial
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.375027Z
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 d946b6ab-d08a-4bbe-8db7-25d3f03942ec · outbound
This paper cites A Tutte polynomial for signed graphs.
Thistlethwaite Theorems for Knotoids and Linkoids A Tutte polynomial for signed graphs
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.357548Z
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 c82143ad-8247-478f-91ec-0d24b23f5f4c · outbound
This paper cites Introduction to virtual knot theory.
Thistlethwaite Theorems for Knotoids and Linkoids Introduction to virtual knot theory
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.340471Z
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 0fe9e530-bf53-4f61-9a1d-7c0e16562c96 · outbound
This paper cites Virtual knot theory.
Thistlethwaite Theorems for Knotoids and Linkoids Virtual knot theory
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.324168Z
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 cb6663dd-7e8e-40f5-ac5f-55902ba25de6 · outbound
This paper cites Framed knotoids and their quantum invariants.
Thistlethwaite Theorems for Knotoids and Linkoids Framed knotoids and their quantum invariants
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.308419Z
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 ae373f61-c890-4443-9450-fd469401eb57 · outbound
This paper cites New quantum invariants of planar knotoids.
Thistlethwaite Theorems for Knotoids and Linkoids New quantum invariants of planar knotoids
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.291019Z
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 21f44e1c-01bb-4073-b8da-426e09c3d991 · outbound
This paper cites Knot polynomials of open and closed curves.
Thistlethwaite Theorems for Knotoids and Linkoids Knot polynomials of open and closed curves
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.274105Z
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 9a4805e8-a5c4-4e8c-b5b6-d580b8385e6d · outbound
This paper cites A twisted Thistleth- waite theorem.
Thistlethwaite Theorems for Knotoids and Linkoids A twisted Thistleth- waite theorem
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.257411Z
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 8bc06c07-5b9f-4f58-a3f6-f48f8bc40157 · outbound
This paper cites A spanning tree expansion for the Jones polynomial.
Thistlethwaite Theorems for Knotoids and Linkoids A spanning tree expansion for the Jones polynomial
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.240187Z
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 7748e532-15be-4fac-ae42-f93c9e8e2f91 · outbound
This paper cites Knotoids.
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:16:05.223141Z
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
Observation 40841a59-b72a-46ab-b0b4-20d614992db6 · inbound
Biquandle Virtual Brackets and Virtual Knotoids cites this paper.
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 2026-08-16T06:30:59.297886+00:00.