Paper Citation Record · LEDGER

Torus knots in adjoint representation and Vogel's universality

As of 18 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 3 inbound Pith citation observations for arXiv:2506.06219.

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pith.paper-citation-record.v1
2506.06219 v1

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measured 47 of 47 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-07T06:04:27.768737Z

measured 50 of 50 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

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Source: paper_references, paper_reference_links, observed 2026-08-06T17:22:32.479060Z

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Source: arxiv_reference, observed 2026-05-15T01:09:37.054603Z

Reference resolution

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Outbound references

Observation 89c0a905-d959-4bc1-b38a-deb501d02ab8 · outbound

This paper cites Vogel,Algebraic structures on modules of diagrams, Preprint (1995), available athttps://webusers.

Torus knots in adjoint representation and Vogel's universality Vogel,Algebraic structures on modules of diagrams, Preprint (1995), available athttps://webusers

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:04:31.878544Z

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Observation 6cf2c497-5b71-4238-bb08-1abc46535467 · outbound

This paper cites Vogel,The Universal Lie algebra, Preprint (1999), available athttps://webusers.imj-prg.fr/ ~pierre.vogel/grenoble-99b.pdf.

Torus knots in adjoint representation and Vogel's universality Vogel,The Universal Lie algebra, Preprint (1999), available athttps://webusers.imj-prg.fr/ ~pierre.vogel/grenoble-99b.pdf

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:21.653992Z

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Observation 40b597ba-fddf-448b-8e69-63ff415f9c09 · outbound

This paper cites Can Yang-Baxter imply Lie algebra?.

Torus knots in adjoint representation and Vogel's universality Can Yang-Baxter imply Lie algebra?

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:21.722635Z

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Observation 19db09db-92ed-43c8-9766-5d5e5ddd1033 · outbound

This paper cites Universality in Chern-Simons theory.

Torus knots in adjoint representation and Vogel's universality Universality in Chern-Simons theory

Reference 4

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Observation 94722acb-46c6-4cc8-9da0-84943b06a03c · outbound

This paper cites Nonperturbative universal Chern-Simons theory.

Torus knots in adjoint representation and Vogel's universality Nonperturbative universal Chern-Simons theory

Reference 5

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Observation 38dc6937-c1dc-48c0-bb28-72f78e3b4707 · outbound

This paper cites Exact Chern-Simons / Topological String duality.

Torus knots in adjoint representation and Vogel's universality Exact Chern-Simons / Topological String duality

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:21.985276Z

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Observation 3ad71e18-add2-4527-891c-4bcab7761f48 · outbound

This paper cites Partition function of Chern-Simons theory as renormalized q-dimension.

Torus knots in adjoint representation and Vogel's universality Partition function of Chern-Simons theory as renormalized q-dimension

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:22.052977Z

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Observation 9e37ae79-0d0c-4433-baf0-97c813ddbd76 · outbound

This paper cites Westbury, Proceedings of the Tenth Oporto Meeting on Geometry, Topology and Physics,18(2001) suppl.

Torus knots in adjoint representation and Vogel's universality Westbury, Proceedings of the Tenth Oporto Meeting on Geometry, Topology and Physics,18(2001) suppl

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:22.114938Z

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Observation bf1932a5-50f0-4f14-9fd6-3395327f3001 · outbound

This paper cites On Universal Quantum Dimensions.

Torus knots in adjoint representation and Vogel's universality On Universal Quantum Dimensions

Reference 9

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Observation 26f37f8e-47b7-4359-90c9-3beff7460a9d · outbound

This paper cites Landsberg, L.

Torus knots in adjoint representation and Vogel's universality Landsberg, L

Reference 10

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Observation 79ae2c2a-4203-4e6a-9281-66af26be6b77 · outbound

This paper cites Casimir eigenvalues for universal Lie algebra.

Torus knots in adjoint representation and Vogel's universality Casimir eigenvalues for universal Lie algebra

Reference 11

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Observation ed8ff389-15b2-4eb9-8f03-52701d85c245 · outbound

This paper cites The uniform structure of $\mathfrak{g}^{\otimes 4}$.

Torus knots in adjoint representation and Vogel's universality The uniform structure of $\mathfrak{g}^{\otimes 4}$

Reference 12

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Observation 547673be-d581-4b4b-8c33-378bc5af4a8c · outbound

This paper cites Projectors on invariant subspaces of representations $\operatorname{ad}^{\otimes 2}$ of Lie algebras $so(N)$ and $sp(2r)$ and Vogel parametrization.

Torus knots in adjoint representation and Vogel's universality Projectors on invariant subspaces of representations $\operatorname{ad}^{\otimes 2}$ of Lie algebras $so(N)$ and $sp(2r)$ and Vogel parametrization

Reference 13

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Observation 7b6acbcc-b6ae-463a-82e1-2a7ba26b0b4e · outbound

This paper cites Split Casimir operator for simple Lie algebras, solutions of Yang-Baxter equations and Vogel parameters.

Torus knots in adjoint representation and Vogel's universality Split Casimir operator for simple Lie algebras, solutions of Yang-Baxter equations and Vogel parameters

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:22.651394Z

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Observation fb781379-2c0a-46a9-b0a6-4aa9efe215e7 · outbound

This paper cites Split Casimir operator for simple Lie algebras in the cube of $\mathsf{ad}$-representation and Vogel parameters.

Torus knots in adjoint representation and Vogel's universality Split Casimir operator for simple Lie algebras in the cube of $\mathsf{ad}$-representation and Vogel parameters

Reference 15

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Observation 351e6ebe-bff6-4706-920f-11e3b10b32f5 · outbound

This paper cites Universal volume of groups and anomaly of Vogel's symmetry.

Torus knots in adjoint representation and Vogel's universality Universal volume of groups and anomaly of Vogel's symmetry

Reference 16

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Observation cd6e8319-783e-4663-b921-8d03e5eb2d60 · outbound

This paper cites On universal knot polynomials.

Torus knots in adjoint representation and Vogel's universality On universal knot polynomials

Reference 17

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Observation b5e2951b-6225-47de-98fe-4b8cba7740a1 · outbound

This paper cites Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots.

Torus knots in adjoint representation and Vogel's universality Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots

Reference 18

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Observation f5d4b7a9-b924-4f05-9dfd-ccc49a57ec51 · outbound

This paper cites Construction of Lie algebra weight system kernel via Vogel algebra.

Torus knots in adjoint representation and Vogel's universality Construction of Lie algebra weight system kernel via Vogel algebra

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:23.044635Z

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Observation 991b824f-4c90-4148-8fb8-7332a1d6f5e8 · outbound

This paper cites Macdonald deformation of Vogel's universality and link hyperpolynomials.

Torus knots in adjoint representation and Vogel's universality Macdonald deformation of Vogel's universality and link hyperpolynomials

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:23.105204Z

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Observation 86dc0a68-6ae2-4ae6-90a7-bf2b0777797c · outbound

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Torus knots in adjoint representation and Vogel's universality Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:04:31.615077Z

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Observation 6a991fbd-5b67-4632-9955-636c820688db · outbound

This paper cites Rosso, V.F.R.

Torus knots in adjoint representation and Vogel's universality Rosso, V.F.R

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:04:31.400029Z

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Observation 732bc735-eeb3-4f0f-b110-2f323d22dad3 · outbound

This paper cites On the Hecke algebras and the colored HOMFLY polynomial.

Torus knots in adjoint representation and Vogel's universality On the Hecke algebras and the colored HOMFLY polynomial

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-07T06:04:29.737202Z

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Observation ec778fe4-7c6a-4278-81f4-f21af6284868 · outbound

This paper cites Chern-Simons Invariants of Torus Links.

Torus knots in adjoint representation and Vogel's universality Chern-Simons Invariants of Torus Links

Reference 24

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Observation 80c3ac1c-8dc5-4f5f-8d4b-c67c9da29c9f · outbound

This paper cites Orthogonal Quantum Group Invariants of Links.

Torus knots in adjoint representation and Vogel's universality Orthogonal Quantum Group Invariants of Links

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-07T06:04:29.460726Z

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Observation 04142e07-6fbd-41cb-b937-b11e5b519d69 · outbound

This paper cites Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid.

Torus knots in adjoint representation and Vogel's universality Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid

Reference 26

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Observation e540de09-d950-4c4c-8f66-ccdfa9014e4d · outbound

This paper cites Murnaghan,The Theory of Group Representations, (The Johns Hopkins Press, Baltimore, 1938).

Torus knots in adjoint representation and Vogel's universality Murnaghan,The Theory of Group Representations, (The Johns Hopkins Press, Baltimore, 1938)

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:04:31.212203Z

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Observation 908153b2-2de5-4702-96bc-ee5f4891de2c · outbound

This paper cites Littlewood,The Theory of Group Characters and Matrix Representations of Groups, (The Clarendon Press, Oxford, 1950.

Torus knots in adjoint representation and Vogel's universality Littlewood,The Theory of Group Characters and Matrix Representations of Groups, (The Clarendon Press, Oxford, 1950

Reference 29

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Observation 70ace452-95b7-4ff6-964e-9e0d23249648 · outbound

This paper cites Character Expansions for the Orthogonal and Symplectic Groups.

Torus knots in adjoint representation and Vogel's universality Character Expansions for the Orthogonal and Symplectic Groups

Reference 30

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Observation 06e3d59d-71ce-451d-b120-fec317744271 · outbound

This paper cites Macdonald,Symmetric functions and Hall polynomials, Oxford University Press, 1995.

Torus knots in adjoint representation and Vogel's universality Macdonald,Symmetric functions and Hall polynomials, Oxford University Press, 1995

Reference 31

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Observation ebcfeb9e-ad53-4937-b4eb-64a3830a8363 · outbound

This paper cites Refined composite invariants of torus knots via DAHA.

Torus knots in adjoint representation and Vogel's universality Refined composite invariants of torus knots via DAHA

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:24.656859Z

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Observation bb2779cc-1f74-4b25-a559-221a6bfd2956 · outbound

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Torus knots in adjoint representation and Vogel's universality Unresolved cited work

Reference 33

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Observation ebdf1c2a-b819-42a0-8e0f-4392cbd9aa69 · outbound

This paper cites Cvitanovic,Group Theory, Princeton University Press, Princeton, NJ, 2004.

Torus knots in adjoint representation and Vogel's universality Cvitanovic,Group Theory, Princeton University Press, Princeton, NJ, 2004

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:04:30.250475Z

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Observation 9d85b5bb-f095-4987-b29b-d2e5f4c311c3 · outbound

This paper cites On duality and negative dimensions in the theory of Lie groups and symmetric spaces.

Torus knots in adjoint representation and Vogel's universality On duality and negative dimensions in the theory of Lie groups and symmetric spaces

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:25.193749Z

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Observation 2fe23bef-1841-4638-9215-d63ed28d5883 · outbound

This paper cites Counting Higher Genus Curves with Crosscaps in Calabi-Yau Orientifolds.

Torus knots in adjoint representation and Vogel's universality Counting Higher Genus Curves with Crosscaps in Calabi-Yau Orientifolds

Reference 36

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Observation fca6e3fe-569c-45f2-bb16-b93304c7fabe · outbound

This paper cites On universal quantum dimensions of certain two-parameter series of representations.

Torus knots in adjoint representation and Vogel's universality On universal quantum dimensions of certain two-parameter series of representations

Reference 37

Resolution: verified exact; local_arxiv, observed 2026-08-07T06:04:29.067197Z

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Observation eec0ca87-f05f-40eb-89a2-4cdae56e94f4 · outbound

This paper cites Superpolynomials for toric knots from evolution induced by cut-and-join operators.

Torus knots in adjoint representation and Vogel's universality Superpolynomials for toric knots from evolution induced by cut-and-join operators

Reference 39

Resolution: verified exact; local_arxiv, observed 2026-08-07T06:04:28.748120Z

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Observation abf7f988-782e-4b18-91f2-82182ea08759 · outbound

This paper cites Colored HOMFLY polynomial via skein theory.

Torus knots in adjoint representation and Vogel's universality Colored HOMFLY polynomial via skein theory

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:26.088873Z

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Observation 797ad03c-d354-42d6-a8fb-cf0c5b689fcf · outbound

This paper cites The Superpolynomial for Knot Homologies.

Torus knots in adjoint representation and Vogel's universality The Superpolynomial for Knot Homologies

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:26.297898Z

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Observation 1a0c0dd3-07ce-41dc-9672-f1cf6fa7b8a1 · outbound

This paper cites HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations.

Torus knots in adjoint representation and Vogel's universality HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:26.466753Z

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Observation 0896f124-3291-4753-a6c5-526f20c9e747 · outbound

This paper cites Evolution method and "differential hierarchy" of colored knot polynomials.

Torus knots in adjoint representation and Vogel's universality Evolution method and "differential hierarchy" of colored knot polynomials

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:26.752554Z

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Observation ad99adb8-c030-4f88-88dd-5e25a6c85c0b · outbound

This paper cites Refined Chern-Simons versus Vogel universality.

Torus knots in adjoint representation and Vogel's universality Refined Chern-Simons versus Vogel universality

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:26.941110Z

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Observation 77a2c582-1518-452b-8549-7ec18f6ea27b · outbound

This paper cites On partition functions of refined Chern-Simons theories on $S^3$.

Torus knots in adjoint representation and Vogel's universality On partition functions of refined Chern-Simons theories on $S^3$

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:27.105295Z

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Observation 68e0ef1f-f22f-41c8-a3d2-20e693fa9689 · outbound

This paper cites Vogel's Universality and its Applications.

Torus knots in adjoint representation and Vogel's universality Vogel's Universality and its Applications

Reference 47

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Observation 4443fa1e-f85e-463b-8911-277e14c56f22 · outbound

This paper cites On Refined Vogel's universality.

Torus knots in adjoint representation and Vogel's universality On Refined Vogel's universality

Reference 48

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Observation 89f1a74d-3b54-4609-89ba-fba9c62f63f2 · outbound

This paper cites Can tangle calculus be applicable to hyperpolynomials?.

Torus knots in adjoint representation and Vogel's universality Can tangle calculus be applicable to hyperpolynomials?

Reference 49

Resolution: verified exact; local_arxiv, observed 2026-08-07T06:04:28.357189Z

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Observation be5dd80a-b5e1-43be-928b-76910b6a6e18 · outbound

This paper cites Hopf superpolynomial from topological vertices.

Torus knots in adjoint representation and Vogel's universality Hopf superpolynomial from topological vertices

Reference 50

Resolution: verified exact; local_arxiv, observed 2026-08-07T06:04:28.022686Z

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Pith citing papers

Observation 65dd86f7-ed96-4fa9-9d8a-d018c8435616 · inbound

Vogel's universality and Macdonald dimensions cites this paper.

Vogel's universality and Macdonald dimensions Torus knots in adjoint representation and Vogel's universality

Reference 18

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Observation 3c2c4adb-b8e9-4ee3-9ffb-bb3904c40b69 · inbound

Racah matrices for the symmetric representation of the SO(5) group cites this paper.

Racah matrices for the symmetric representation of the SO(5) group Torus knots in adjoint representation and Vogel's universality

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-15T01:09:37.056037Z

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Observation d8e22059-d9fe-4d6d-a8a1-d7c84f9b9679 · inbound

A note on universality in refined Chern-Simons theory cites this paper.

A note on universality in refined Chern-Simons theory Torus knots in adjoint representation and Vogel's universality

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-13T03:47:12.788737Z

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