Paper Citation Record · LEDGER

On the classification and irreducibility of $2$-local representations of the twin group $T_n$

As of 21 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 3 inbound Pith citation observations for arXiv:2508.14505.

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

pith.paper-citation-record.v1
2508.14505 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T18:51:29.455178Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T18:51:28.139636Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-14T01:48:36.001695Z

Reference resolution

23 of 23 outbound references displayed

verified exact0
verified fuzzy15
unresolved8
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 866c7c38-1434-40d6-8f17-957e401dc74c · outbound

This paper cites On the classification and irreducibility of $2$-local representations of the twin group $T_n$.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ On the classification and irreducibility of $2$-local representations of the twin group $T_n$

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-05T18:51:28.139636Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d84cba72-556a-484e-8f94-105fae223067 · outbound

This paper cites , sn� 1 and the following relations.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ , sn� 1 and the following relations

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:31.344412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6561741c-aa05-4a3f-9226-205eed900e87 · outbound

This paper cites an unresolved cited work.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:51:31.329422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 29abc0ce-4963-4285-9287-69f54fe382ca · outbound

This paper cites We first investigate their reducibility and establish that all such representations admit a non-trivial invariant subspace.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ We first investigate their reducibility and establish that all such representations admit a non-trivial invariant subspace

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:31.314467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 355b1da5-4c1e-4795-81bd-8a3e2d07e643 · outbound

This paper cites To this end, we first present several propositions, lemmas, and theorems, which will lead us to the statement of our main result.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ To this end, we first present several propositions, lemmas, and theorems, which will lead us to the statement of our main result

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:31.298737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9e71dc6f-af5c-4d72-87de-1f56c1a0412d · outbound

This paper cites Thus, the subspace ⟨v2⟩ is invariant under the action of S2 if and only if a = 1.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Thus, the subspace ⟨v2⟩ is invariant under the action of S2 if and only if a = 1

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:31.282778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 938879c1-ee93-4a54-a2bc-ef2b49acb498 · outbound

This paper cites Birman, �� , Annals of Mathematics Studies, Prince- ton University Press, (1974).

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Birman, �� , Annals of Mathematics Studies, Prince- ton University Press, (1974)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:31.267926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 32217332-2cef-4cfe-baf9-03d21c4b0f38 · outbound

This paper cites Crisp and L.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Crisp and L

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:31.251877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation db425925-4c5f-45bc-af60-97315627336a · outbound

This paper cites Funar, �� , Topology and its Applications, 156, (2009), 2504–2520.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Funar, �� , Topology and its Applications, 156, (2009), 2504–2520

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:31.235097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a7edda1e-d9ba-4b6c-8cfa-692faae2384b · outbound

This paper cites Golub, and C.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Golub, and C

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:31.218890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3d7bcc8c-a2b7-4624-8de9-6054bba70a04 · outbound

This paper cites Humphreys, �� , Graduate Studies in Mathematics, 94, American Mathematical Society, (2008).

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Humphreys, �� , Graduate Studies in Mathematics, 94, American Mathematical Society, (2008)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:31.046099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a3999ec2-a041-47ec-a188-1305ffce1cf9 · outbound

This paper cites On representations of the multi-virtual braid group $M_kVB_n$ and the multi-welded braid group $M_kWB_n$.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ On representations of the multi-virtual braid group $M_kVB_n$ and the multi-welded braid group $M_kWB_n$

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-05T18:51:28.801335Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4390e1c6-66ac-46f3-abb9-f1e5227a0c6b · outbound

This paper cites Khovanov, �� , Transactions of the American Mathematical Society, 349, (1997), 2297–2315.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Khovanov, �� , Transactions of the American Mathematical Society, 349, (1997), 2297–2315

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:30.773111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ba860188-18d2-498f-a314-8e1d547568a8 · outbound

This paper cites Lopatkin, and V.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Lopatkin, and V

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:30.508371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f1051da4-9ee8-4bdf-9124-d7aae915cdfe · outbound

This paper cites Lopatkin, �� , Algebra and Discrete Mathematics, 30, (2020), 1–10.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Lopatkin, �� , Algebra and Discrete Mathematics, 30, (2020), 1–10

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:30.229776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 03175d6e-8ccc-4667-bedf-7aba95e37858 · outbound

This paper cites Classification of Homogeneous Local Representations of the Singular Braid Monoid.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Classification of Homogeneous Local Representations of the Singular Braid Monoid

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-05T18:51:29.057516Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84eb540c-412b-4e5e-8d92-326f46832ccf · outbound

This paper cites Mikhalchishina, �� , Siberian Mathematical Journal, 54, (2013), 666–678.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Mikhalchishina, �� , Siberian Mathematical Journal, 54, (2013), 666–678

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:30.066077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fbcccc9c-30ec-4514-9327-a0d55c14fd26 · outbound

This paper cites an unresolved cited work.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:51:29.937819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 55800697-9612-4085-b72d-316c413a3691 · outbound

This paper cites Nasser, �� Φ�� Bn �� SMn, Vietnam Journal of Mathematics, (2024), 1–12.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Nasser, �� Φ�� Bn �� SMn, Vietnam Journal of Mathematics, (2024), 1–12

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:29.817662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5a345db4-b4af-4c61-a848-2d126aec7289 · outbound

This paper cites Local Representations of the Flat Virtual Braid Group.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Local Representations of the Flat Virtual Braid Group

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-05T18:51:29.292640Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f119825a-e9d2-4cec-8697-b1eef30678b8 · outbound

This paper cites Matrix representations of the twisted virtual braid group and its extensions.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Matrix representations of the twisted virtual braid group and its extensions

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-05T18:51:29.351355Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7fc556e4-24c3-4232-9d16-7b8459f32053 · outbound

This paper cites Twin groups representations.

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Twin groups representations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-05T18:51:29.381924Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 226ca1db-37c3-4426-8738-68e4bbc6aa17 · outbound

This paper cites Serre, �� , Springer, (1977).

On the classification and irreducibility of $2$-local representations of the twin group $T_n$ Serre, �� , Springer, (1977)

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:51:29.679067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation 866c7c38-1434-40d6-8f17-957e401dc74c · inbound