Paper Citation Record · LEDGER

Braid closure union braid axis is ribbon concordance minimal

As of 21 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 0 inbound Pith citation observations for arXiv:2607.14030.

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

pith.paper-citation-record.v1
2607.14030 v1

Coverage vector

measured 51 of 51 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T03:13:24.778739Z

measured 51 of 51 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 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

51 of 51 outbound references displayed

verified exact21
verified fuzzy0
unresolved29
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8ce9256e-27f0-4a6a-858b-65616818834f · outbound

This paper cites 2021 , PAGES =.

Braid closure union braid axis is ribbon concordance minimal 2021 , PAGES =

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:19.011396Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 90cf9584-576a-4b48-a810-9912251105c6 · outbound

This paper cites Elisenda and Licata, Anthony M.

Braid closure union braid axis is ribbon concordance minimal Elisenda and Licata, Anthony M

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:19.111897Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe367d90-de87-4abb-aef9-4874784aeed3 · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:19.258316Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 63aff4a6-bfe1-4473-8229-288c46055dbe · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:19.332791Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf30cfc7-ce79-4f31-b4f5-c920b6ebdd32 · outbound

This paper cites Elisenda and Ni, Yi , TITLE =.

Braid closure union braid axis is ribbon concordance minimal Elisenda and Ni, Yi , TITLE =

Reference 5

Resolution: verified exact; doi, observed 2026-08-02T03:19:16.212807Z

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 2b650420-b49d-433e-a7e1-3f5b2cfceeb4 · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 6

Resolution: verified exact; doi, observed 2026-08-02T03:19:16.036189Z

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 f83cdd58-91e8-4a7f-8987-94f27f3768f3 · outbound

This paper cites , TITLE =.

Braid closure union braid axis is ribbon concordance minimal , TITLE =

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:19.549027Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfaffbaa-c3e4-4d24-8a66-44096e709e4d · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:19.656267Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9609ac76-7ec8-4f1b-b5fa-241b8f7160f9 · outbound

This paper cites arXiv preprint , YEAR =.

Braid closure union braid axis is ribbon concordance minimal arXiv preprint , YEAR =

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:19.852265Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1bc56cfb-15ed-47ec-aab7-b1b41ee641e0 · outbound

This paper cites , TITLE =.

Braid closure union braid axis is ribbon concordance minimal , TITLE =

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:19.936793Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c8746c9-202c-4620-8032-72e95d0d287b · outbound

This paper cites arXiv preprint , YEAR =.

Braid closure union braid axis is ribbon concordance minimal arXiv preprint , YEAR =

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:19.965974Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a828301-25ae-42d7-b1e6-2085c15bf590 · outbound

This paper cites Pacific J.

Braid closure union braid axis is ribbon concordance minimal Pacific J

Reference 12

Resolution: verified exact; doi, observed 2026-08-02T03:19:15.877546Z

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 626bb4b2-276e-497c-afc3-e0cfce38325d · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 13

Resolution: verified exact; doi, observed 2026-08-02T03:19:15.723109Z

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 0d4f7edb-1ade-451a-a121-5071d7e96490 · outbound

This paper cites Michael , TITLE =.

Braid closure union braid axis is ribbon concordance minimal Michael , TITLE =

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:20.359952Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e55db33a-47b7-412c-813c-e8f8f262f964 · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 15

Resolution: verified exact; doi, observed 2026-08-02T03:19:15.586577Z

Source-reported events for the cited work

correction dated 2020-04-23. Source: crossref record 10.1112/blms.12333->10.1112/blms.12303:correction, observed 2026-07-11T03:16:05.455175+00:00. This notice travels one citation hop only.

Observation 56a38f73-0c23-499b-a6c6-d693e0bc0ec6 · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 16

Resolution: verified exact; doi, observed 2026-08-02T03:19:15.433175Z

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 b51fcc48-4c71-48b1-bbdc-672c9d950404 · outbound

This paper cites , TITLE =.

Braid closure union braid axis is ribbon concordance minimal , TITLE =

Reference 17

Resolution: verified exact; doi, observed 2026-08-02T03:19:15.302380Z

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 a0725f38-d1d8-4c36-a24c-045674b71ef9 · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:20.812035Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1521f9f-fc53-4b8e-b512-184b600b974a · outbound

This paper cites and Sivek, Steven , TITLE =.

Braid closure union braid axis is ribbon concordance minimal and Sivek, Steven , TITLE =

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:20.934676Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 846662be-7439-4720-abc5-4733d428377d · outbound

This paper cites and Hanselman, John and Sivek, Steven , TITLE =.

Braid closure union braid axis is ribbon concordance minimal and Hanselman, John and Sivek, Steven , TITLE =

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:21.073745Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73aa9e8b-d2d7-45df-a3ce-72157e51e188 · outbound

This paper cites arXiv preprint , YEAR =.

Braid closure union braid axis is ribbon concordance minimal arXiv preprint , YEAR =

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:21.214874Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a5fc42a-eab9-483a-abbd-95dde49ebaad · outbound

This paper cites and Przytycki, J\'ozef H.

Braid closure union braid axis is ribbon concordance minimal and Przytycki, J\'ozef H

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:21.335740Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 45699be3-a5c2-4845-9847-754a2f5a44e5 · outbound

This paper cites Duke Math.

Braid closure union braid axis is ribbon concordance minimal Duke Math

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:21.485062Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0469e77d-44ae-4b06-9973-0dfef4c565d8 · outbound

This paper cites [2026] 2026 , PAGES =.

Braid closure union braid axis is ribbon concordance minimal [2026] 2026 , PAGES =

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:21.617959Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aae028f5-a3bb-4ef6-b5f7-9c1fee2f4da6 · outbound

This paper cites arXiv preprint , YEAR =.

Braid closure union braid axis is ribbon concordance minimal arXiv preprint , YEAR =

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:21.712455Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation abf7fe51-dddd-4404-9ee2-cd9869470f77 · outbound

This paper cites Topology Appl.

Braid closure union braid axis is ribbon concordance minimal Topology Appl

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:21.813398Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 761472b2-ef11-4362-9d1a-975e3b452c94 · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 27

Resolution: verified exact; doi, observed 2026-08-02T03:19:15.130222Z

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 ef6d48bc-683d-495b-a51d-0fd402793a89 · outbound

This paper cites and Gong, Sherry , TITLE =.

Braid closure union braid axis is ribbon concordance minimal and Gong, Sherry , TITLE =

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:22.062520Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78040cfc-93ff-4616-b2fe-325484d536a4 · outbound

This paper cites and Levine, Adam Simon and Sarkar, Sucharit , TITLE =.

Braid closure union braid axis is ribbon concordance minimal and Levine, Adam Simon and Sarkar, Sucharit , TITLE =

Reference 29

Resolution: verified exact; doi, observed 2026-08-02T03:19:14.946624Z

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 2915c377-3ebe-4bfb-8d87-df262d4e877c · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:22.276796Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b7efc618-4572-4460-a88a-0e1b8d746e5e · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:22.339016Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3cd9aef7-56b0-4725-bc76-afd760656950 · outbound

This paper cites , TITLE =.

Braid closure union braid axis is ribbon concordance minimal , TITLE =

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:22.481658Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0a36a5ac-0c77-444e-b17f-01c1b234e221 · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 33

Resolution: verified exact; doi, observed 2026-08-02T03:19:14.809865Z

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 1efff873-ccc3-4353-841a-94709a7072fd · outbound

This paper cites , TITLE =.

Braid closure union braid axis is ribbon concordance minimal , TITLE =

Reference 34

Resolution: verified exact; doi, observed 2026-08-02T03:19:14.657294Z

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 a3b18871-7797-4374-a52e-51f5969cd083 · outbound

This paper cites arXiv preprint , YEAR =.

Braid closure union braid axis is ribbon concordance minimal arXiv preprint , YEAR =

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:22.895984Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af927130-414f-4052-8fa1-2ebf6505b72e · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 36

Resolution: verified exact; doi, observed 2026-08-02T03:19:14.514593Z

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 79d15b7d-a5fe-462d-8174-f546772c848a · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:23.086201Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e7c180ec-9d90-4c1f-83d3-37fe1a9fe674 · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:23.205176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c5f0401-0c3a-47f6-966a-cbfdc6acd44c · outbound

This paper cites , TITLE =.

Braid closure union braid axis is ribbon concordance minimal , TITLE =

Reference 39

Resolution: verified exact; doi, observed 2026-08-02T03:19:14.397965Z

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 caa5b850-e8b6-4b26-a239-369069d29bca · outbound

This paper cites , TITLE =.

Braid closure union braid axis is ribbon concordance minimal , TITLE =

Reference 40

Resolution: malformed identifier; doi_truncated, observed 2026-08-02T03:19:14.278494Z

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 42018447-53cb-4c9a-a67a-4ba82653364c · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 41

Resolution: verified exact; doi, observed 2026-08-02T03:19:14.130990Z

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 1ff31fca-8951-4162-9c31-e9ae14555dc0 · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:23.773348Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bb6d46a1-364b-423d-892c-97d879601723 · outbound

This paper cites and Grigsby, J.

Braid closure union braid axis is ribbon concordance minimal and Grigsby, J

Reference 43

Resolution: verified exact; doi, observed 2026-08-02T03:19:13.974748Z

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 99c81327-6f11-4a6f-b984-a6465fe7e7b5 · outbound

This paper cites Quantum Topol.

Braid closure union braid axis is ribbon concordance minimal Quantum Topol

Reference 44

Resolution: verified exact; doi, observed 2026-08-02T03:19:13.810169Z

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 588547d7-a9de-4839-ad81-9e58cd4d72eb · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 45

Resolution: verified exact; doi, observed 2026-08-02T03:19:13.634239Z

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 6d81ecfc-32f0-4fc4-9ce5-acbfb2129282 · outbound

This paper cites arXiv preprint , YEAR =.

Braid closure union braid axis is ribbon concordance minimal arXiv preprint , YEAR =

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:24.104332Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7631ea7a-6006-4cc4-91e7-b31b385d9c17 · outbound

This paper cites Pacific J.

Braid closure union braid axis is ribbon concordance minimal Pacific J

Reference 47

Resolution: verified exact; doi, observed 2026-08-02T03:19:13.469047Z

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 ea046243-ab70-433d-b997-6db176ed7774 · outbound

This paper cites , TITLE =.

Braid closure union braid axis is ribbon concordance minimal , TITLE =

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-02T03:13:24.403891Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation edc3a008-cd12-4dc1-b12e-a0d52e7c4a99 · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 49

Resolution: verified exact; doi, observed 2026-08-02T03:19:13.343288Z

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 e0e50261-018e-4e58-a569-6fba6a31f33e · outbound

This paper cites an unresolved cited work.

Braid closure union braid axis is ribbon concordance minimal Unresolved cited work

Reference 50

Resolution: verified exact; doi, observed 2026-08-02T03:19:13.249141Z

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 6aa13356-0a4f-4970-8eb7-cf90f83d9910 · outbound

This paper cites , TITLE =.

Braid closure union braid axis is ribbon concordance minimal , TITLE =

Reference 51

Resolution: verified exact; doi, observed 2026-08-02T03:19:13.131268Z

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

No inbound Pith citation observations are available.