Paper Citation Record · LEDGER

Classification of Homogeneous Local Representations of the Singular Braid Monoid

As of 22 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 3 inbound Pith citation observations for arXiv:2501.13404.

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

pith.paper-citation-record.v1
2501.13404 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T16:15:29.066530Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:08:31.773175Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-19T04:12:02.532802Z

Reference resolution

17 of 17 outbound references displayed

verified exact2
verified fuzzy11
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 78f8faa3-2f7d-4004-88e0-23d3434f7293 · outbound

This paper cites Baez, Link invariants of ﬁnite type and perturbation theory , Lett.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Baez, Link invariants of ﬁnite type and perturbation theory , Lett

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:15:29.243092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation aca53880-eaf9-4327-8dec-ec377fb8dcdf · outbound

This paper cites Bardakov, P.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Bardakov, P

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:15:29.234990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0c1fc57c-457d-4adf-8c96-4ad4d9017ed8 · outbound

This paper cites Bardakov, N.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Bardakov, N

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:15:29.226680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation debfc7b3-f95b-46cc-8759-c26d73774db0 · outbound

This paper cites Birman, New points of view in knot theory , Bull.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Birman, New points of view in knot theory , Bull

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:15:29.219035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 51d2c972-8aab-4f68-b735-b66937267434 · outbound

This paper cites Burau, Braids, Uber Zopfgruppen and gleichsinnig verdrillte Verk ettungen, Abh.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Burau, Braids, Uber Zopfgruppen and gleichsinnig verdrillte Verk ettungen, Abh

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:15:29.210141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dfcd9f63-ddf6-4330-9687-707647a1a149 · outbound

This paper cites Chreif, M.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Chreif, M

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:15:29.200710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5795edad-ce76-4216-82aa-c4aa88e1a189 · outbound

This paper cites The Word Problem for the Singular Braid Monoid.

Classification of Homogeneous Local Representations of the Singular Braid Monoid The Word Problem for the Singular Braid Monoid

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-10T16:15:29.118630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a8a0a7f9-c938-4547-add1-bc1fe45593fd · outbound

This paper cites A Faithful Representation of the Singular Braid Monoid on Three Strands.

Classification of Homogeneous Local Representations of the Singular Braid Monoid A Faithful Representation of the Singular Braid Monoid on Three Strands

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-10T16:15:29.106618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5c2609dd-f7ab-440e-a65d-ecc9b1a1c60c · outbound

This paper cites an unresolved cited work.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:15:29.191627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4b45592a-b8b8-4fdf-8d20-b005831ca80b · outbound

This paper cites Formanek, Braid group representations of low degree , Proc.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Formanek, Braid group representations of low degree , Proc

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:15:29.182445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b830d634-dc02-46e4-842e-7a0b54afff72 · outbound

This paper cites Gemein, Representations of the singular braid monoid and group inva riants of singular knots, Topology and its Applications, 114 (2001), 117–140.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Gemein, Representations of the singular braid monoid and group inva riants of singular knots, Topology and its Applications, 114 (2001), 117–140

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:15:29.173017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 07e96628-a912-4b01-9e29-a45b8e0fc153 · outbound

This paper cites an unresolved cited work.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-10T16:15:29.163035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b789ee87-7b92-404e-b8fe-ccb3cfee1890 · outbound

This paper cites Mikhalchishina, Local representations of braid groups , Sib.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Mikhalchishina, Local representations of braid groups , Sib

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-10T16:15:29.053730Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c5e7fb9-7388-4d4e-aa03-da53d37e18cf · outbound

This paper cites On the Faithfulness of a Family of Representations of the Singular Braid Monoid $SM_n$.

Classification of Homogeneous Local Representations of the Singular Braid Monoid On the Faithfulness of a Family of Representations of the Singular Braid Monoid $SM_n$

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T16:15:29.056922Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ed2c4087-c092-499e-8776-3f1dbaf98936 · outbound

This paper cites Nasser, Necessary and suﬃcient conditions for the irreducibility o f a linear representation of the braid group Bn, Arab.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Nasser, Necessary and suﬃcient conditions for the irreducibility o f a linear representation of the braid group Bn, Arab

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:15:29.148661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7426bcf7-8046-455a-b0de-b48a9c7c3b72 · outbound

This paper cites Nasser, Local Extensions and Φ -Type Extensions of Some Local Representations of the Braid Group Bn to the Singular Braid Monoid SMn, Accepted in Vietnam Journal of Math- ematics.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Nasser, Local Extensions and Φ -Type Extensions of Some Local Representations of the Braid Group Bn to the Singular Braid Monoid SMn, Accepted in Vietnam Journal of Math- ematics

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:15:29.138623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 12b16c3c-1357-4f27-af3f-293fcaae3d1a · outbound

This paper cites Paris The proof of Birman ’s conjecture on singular braid monoids, Geom.

Classification of Homogeneous Local Representations of the Singular Braid Monoid Paris The proof of Birman ’s conjecture on singular braid monoids, Geom

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T16:15:29.128859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

Observation 22e98dd9-18a1-4c3f-a22a-07b0221c16dd · inbound

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

Matrix representations of the twisted virtual braid group and its extensions Classification of Homogeneous Local Representations of the Singular Braid Monoid

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T11:08:31.773175Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba4e7e25-f5ea-46e7-a11c-9a7c47755cac · inbound

Twin groups representations cites this paper.

Twin groups representations Classification of Homogeneous Local Representations of the Singular Braid Monoid

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-19T04:12:02.534512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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

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

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.