Paper Citation Record · LEDGER

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence

As of 8 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2601.02323.

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

pith.paper-citation-record.v1
2601.02323 v3

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T12:41:54.210261Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

12 of 12 outbound references displayed

verified exact0
verified fuzzy0
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b19ccd96-0d93-42a2-ba42-01e8a0e1cad1 · outbound

This paper cites Artin, Theorie der Z¨ opfe, Abh.

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence Artin, Theorie der Z¨ opfe, Abh

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:52.896546Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d191bca0-5fbd-4a37-bcee-440de5d8fc7f · outbound

This paper cites Artin, Theory of braids, Ann.

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence Artin, Theory of braids, Ann

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:53.003679Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9427e106-1a04-4228-9c6c-b2380d47d310 · outbound

This paper cites Berger, Hurwitz equivalence in dihedral groups, Electron.

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence Berger, Hurwitz equivalence in dihedral groups, Electron

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:53.158519Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e4fcfee-0450-4d2f-9887-5173ad65dfee · outbound

This paper cites Burillo, M.

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence Burillo, M

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:53.236500Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1165a3a-897a-475a-b5cd-c743271f0617 · outbound

This paper cites Crossing Matrices of Positive Braids.

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence Crossing Matrices of Positive Braids

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:53.372784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22419a89-e0c3-42aa-bd05-1ab575a4e8c8 · outbound

This paper cites Kamada, Braid and Knot Theory in Dimension Four, Math.

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence Kamada, Braid and Knot Theory in Dimension Four, Math

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:53.498189Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9427ff59-b862-404a-98e2-6b053c6536f3 · outbound

This paper cites The Hurwitz Equivalence Problem is Undecidable.

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence The Hurwitz Equivalence Problem is Undecidable

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:53.643399Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ad7935c0-15ef-4c17-bd61-a26181092c02 · outbound

This paper cites Ozawa, A.

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence Ozawa, A

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:53.762137Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c591bedf-918b-49bf-a5b2-087427f24b24 · outbound

This paper cites Shimizu, Determinant of the crossing matrix of a braid, arXiv:2509.08464 (2025).

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence Shimizu, Determinant of the crossing matrix of a braid, arXiv:2509.08464 (2025)

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:53.914365Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f25b2fa-8674-4dde-b441-040ad5f277f5 · outbound

This paper cites Shimizu, A.

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence Shimizu, A

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:54.054209Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b9ab0b93-8983-4e28-af73-8adb7cc43b29 · outbound

This paper cites Shimizu and Y.

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence Shimizu and Y

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:54.097855Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba062023-a18a-47ff-92dd-7e1e8f6384b6 · outbound

This paper cites Shimizu and Y.

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence Shimizu and Y

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T12:41:54.210261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.