Paper Citation Record · LEDGER

A Hopf algebra on permutations with a coupling product

As of 19 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2607.23345.

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

pith.paper-citation-record.v1
2607.23345 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-31T23:53:50.255701Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

23 of 23 outbound references displayed

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verified fuzzy0
unresolved23
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External citation measurements

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Outbound references

Observation 86333a4f-f321-4532-8f21-45c011e12a23 · outbound

This paper cites Aguiar, N.

A Hopf algebra on permutations with a coupling product Aguiar, N

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:47.728258Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4dd1271-feff-41ad-8edc-c362083f63d1 · outbound

This paper cites Aguiar and R.

A Hopf algebra on permutations with a coupling product Aguiar and R

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:47.835407Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70ec9e78-04b1-453f-8bcc-7b0b39a09fff · outbound

This paper cites Aguiar and F.

A Hopf algebra on permutations with a coupling product Aguiar and F

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:47.961176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4525ef5e-33ea-4c1d-aef8-01c6b606e6de · outbound

This paper cites Aliniaeifard and N.

A Hopf algebra on permutations with a coupling product Aliniaeifard and N

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:48.081563Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b0c177a-3846-431c-8aea-7c00b41d3ae5 · outbound

This paper cites The hyperoctahedral quantum group.

A Hopf algebra on permutations with a coupling product The hyperoctahedral quantum group

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:48.202473Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e001d488-baca-41b4-a75b-2c0c8b52d42a · outbound

This paper cites Bergeron and M.

A Hopf algebra on permutations with a coupling product Bergeron and M

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:48.328234Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d038ac7c-9db8-40a3-9b9d-54a8e122b6ea · outbound

This paper cites Bergeron, R.

A Hopf algebra on permutations with a coupling product Bergeron, R

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:48.430821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48e6855d-4127-459f-8264-f122961349f9 · outbound

This paper cites Dong and H.

A Hopf algebra on permutations with a coupling product Dong and H

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:48.501927Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f36d82f3-fa66-40d8-8619-4ee236a035eb · outbound

This paper cites Foissy, Free and cofree Hopf algebras.J.

A Hopf algebra on permutations with a coupling product Foissy, Free and cofree Hopf algebras.J

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:48.591188Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8ff934c3-7de6-4b63-ad95-18f3b84868ff · outbound

This paper cites Grossman and R.

A Hopf algebra on permutations with a coupling product Grossman and R

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:48.699589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd9dcf5c-2fd6-4391-9fbb-60e6d4f07ba1 · outbound

This paper cites Hopf, ¨Uber die Topologie der Gruppen-Mannigfaltigkeiten und ihrer Ver- allgemeinerungen,Ann.

A Hopf algebra on permutations with a coupling product Hopf, ¨Uber die Topologie der Gruppen-Mannigfaltigkeiten und ihrer Ver- allgemeinerungen,Ann

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:48.809381Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea1d6b62-4ee1-4afb-9e5a-f11b370dbb7c · outbound

This paper cites Liu and H.

A Hopf algebra on permutations with a coupling product Liu and H

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:48.927145Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 250b8d52-557c-4e17-b8f1-013bc54b36a5 · outbound

This paper cites Loday and M.

A Hopf algebra on permutations with a coupling product Loday and M

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:49.062164Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55ed34c8-1f9e-4243-88ea-202e08786a43 · outbound

This paper cites Malvenuto and C.

A Hopf algebra on permutations with a coupling product Malvenuto and C

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:49.209142Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7e8b3aba-4d78-4ab7-80ed-de6544750179 · outbound

This paper cites Zhao and H.

A Hopf algebra on permutations with a coupling product Zhao and H

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:49.325902Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aa16c369-6558-45f5-9b7d-9b22fd7d7c43 · outbound

This paper cites A Hopf algebra of parking functions.

A Hopf algebra on permutations with a coupling product A Hopf algebra of parking functions

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:49.449092Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9af2ddd6-6862-4763-a4d6-fff58d4340dc · outbound

This paper cites Reutenauer, Free Lie algebras.

A Hopf algebra on permutations with a coupling product Reutenauer, Free Lie algebras

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:49.583336Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a2924f2f-b064-45e0-b011-f441fb2dc53c · outbound

This paper cites Trautman, Clifford algebras and their representations.

A Hopf algebra on permutations with a coupling product Trautman, Clifford algebras and their representations

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:49.681936Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4667527e-23db-49fe-8fab-3892d4b84649 · outbound

This paper cites Takeuchi, Free Hopf algebras generated by coalgebras.J.

A Hopf algebra on permutations with a coupling product Takeuchi, Free Hopf algebras generated by coalgebras.J

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:49.785855Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d5e297b-0c5f-4662-85f1-5c7fb3f7f564 · outbound

This paper cites van den Hijligenberg and R.

A Hopf algebra on permutations with a coupling product van den Hijligenberg and R

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:49.902066Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21df3962-feba-46c3-be87-8e987e8a2779 · outbound

This paper cites an unresolved cited work.

A Hopf algebra on permutations with a coupling product Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:49.986879Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b6df87d-2b2f-40b3-8f23-e6b1a4a86dbd · outbound

This paper cites Song and H.

A Hopf algebra on permutations with a coupling product Song and H

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:50.120816Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6389b2cc-41f5-4e43-869a-b2a8c434330e · outbound

This paper cites Yuan and H.

A Hopf algebra on permutations with a coupling product Yuan and H

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-31T23:53:50.255701Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.