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Paper Citation Record · LEDGER

Profiles of Critical Flat Ribbon Knots

As of 8 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2506.04403.

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

pith.paper-citation-record.v1
2506.04403 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:50:55.617197Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

18 of 18 outbound references displayed

  • verified exact3
  • verified fuzzy10
  • unresolved5
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c607ade2-0b16-4be8-b3d1-bbca3cae009d · outbound

This paper cites Adams, A.

Profiles of Critical Flat Ribbon Knots Adams, A

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:55.925587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.549009Z digest=sha256:ab1e8c929c149a7e8c3c1bdf54bbe88d656730c25539cd0e2168853aac3169c4

Observation 618a174b-f8b7-4610-84fb-0160503b0dff · outbound

This paper cites Ayala, D.

Profiles of Critical Flat Ribbon Knots Ayala, D

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-07T10:50:55.554131Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:50:55.554131Z digest=sha256:bddc6c2cb05f13486e4e0389ec4068b4f4ca5b137cbe412b13fe8baa1fa44eb9

Observation 395365c2-07f8-433f-b7f2-5506309f52fd · outbound

This paper cites Cantarella, J.H.G.

Profiles of Critical Flat Ribbon Knots Cantarella, J.H.G

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:55.915843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.557627Z digest=sha256:255c0010ade059ea04737b3fb7a503f98062b0a7998724c43323a47aef9251b2

Observation f50f583f-3562-4fac-8856-6961e6f4fb47 · outbound

This paper cites Cantarella, R.B.

Profiles of Critical Flat Ribbon Knots Cantarella, R.B

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:55.905377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.561568Z digest=sha256:950a76b45e3cac4d52b894326624f29707f039843ce94c02e9cb80d87baf79a4

Observation bbce51c3-41dd-4afe-a456-ff3ac286f39b · outbound

This paper cites Evans, V.

Profiles of Critical Flat Ribbon Knots Evans, V

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:55.895383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.566425Z digest=sha256:45a067aa8effce442327fcb05f7078804b12597e535069013813ca6b5da6605c

Observation 8c3cd286-f356-459f-b810-1b0aa950e11b · outbound

This paper cites an unresolved cited work.

Profiles of Critical Flat Ribbon Knots Unresolved cited work

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-07T10:50:55.570227Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:50:55.570227Z digest=sha256:92b89305cff6f20bbef9d15281ab9769c4c2e7050028bdf060252dc55eb2fb03

Observation fc75044f-e904-42c1-9b21-05a6e36e492b · outbound

This paper cites Folded ribbon knots in the plane.

Profiles of Critical Flat Ribbon Knots Folded ribbon knots in the plane

Reference 7

Resolution
verified exact
local_arxiv, observed 2026-08-07T10:50:55.692704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.575516Z digest=sha256:83611d419dc26b20c905bbf8b4cefab5d28a6589c12d9b090405a136f16db83e

Observation 99c53e86-881b-4cd9-b3f3-c9c105efc4b7 · outbound

This paper cites an unresolved cited work.

Profiles of Critical Flat Ribbon Knots Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:50:55.885029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.580983Z digest=sha256:46b08a1c96751b75c349df8fc9b48912061639bec028679be2a105ede13846f5

Observation bc82bb0c-abab-4bbd-9f3e-16c628fee52a · outbound

This paper cites Gonzalez, J.H.

Profiles of Critical Flat Ribbon Knots Gonzalez, J.H

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:55.874756Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.584964Z digest=sha256:ce26f151e0efa8063afd50c036fce93af10b7dcfd45e37a6c5c4704d9aeb8a33

Observation b1b0aab2-9bd6-4c3d-a21d-cd83cceabd3e · outbound

This paper cites Kauffman, Minimal flat knotted ribbons, in Series on Knots and Everything, Physical and Numerical Models in Knot Theory, World Scientific Publishing, 2005, pp.

Profiles of Critical Flat Ribbon Knots Kauffman, Minimal flat knotted ribbons, in Series on Knots and Everything, Physical and Numerical Models in Knot Theory, World Scientific Publishing, 2005, pp

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:55.862421Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.588638Z digest=sha256:74493d507c6df468688976b72246257e76e075f181ff4ebde2fba0de7e0fde58

Observation 152e81e4-2e57-4127-8e16-218a75185ffa · outbound

This paper cites A Gordian Pair of Links.

Profiles of Critical Flat Ribbon Knots A Gordian Pair of Links

Reference 11

Resolution
verified exact
doi, observed 2026-08-07T10:50:55.650665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.592111Z digest=sha256:db35cd26f871f8bf7df30ab3b08ae13b1772f26ca3b14a05407d4b65cd407a50

Observation 1f5c3b92-4c5f-4e27-8c7a-c28bf6acd78f · outbound

This paper cites Litherland, J.

Profiles of Critical Flat Ribbon Knots Litherland, J

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-07T10:50:55.595271Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T10:50:55.595271Z digest=sha256:579b5a5c6dbf8971db869fb0b25e6e6c7744edb609303ec86d2659957902af7d

Observation 851e3201-892f-4595-940e-15886eab1a1f · outbound

This paper cites Lomonaco and L.

Profiles of Critical Flat Ribbon Knots Lomonaco and L

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:55.849827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.599056Z digest=sha256:137ae0ec2d07c6f1164b5dc99df3050e800b7086788ed1020ba47cb928b9b7a5

Observation ad008074-2f67-4a26-ba7d-7b15e2d38b39 · outbound

This paper cites Grosberg and S.

Profiles of Critical Flat Ribbon Knots Grosberg and S

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:55.836597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.603151Z digest=sha256:a3f5ff90b186f6924d6d1e803d871216b99f6c0d3997a0019c05111318bff543

Observation ff9c9907-ae1c-4912-adb8-352e263059e5 · outbound

This paper cites Jung, Man & His Symbols, Bantam Doubleday Dell Publishing Group, 1997.

Profiles of Critical Flat Ribbon Knots Jung, Man & His Symbols, Bantam Doubleday Dell Publishing Group, 1997

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:55.824422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.606309Z digest=sha256:cfad82aaca858f706f1972f80392860b8a84f2187b00e4030e79f2471977e033

Observation 6ac15091-d277-4186-8362-c5830771470c · outbound

This paper cites Statistics of knots and entangled random walks.

Profiles of Critical Flat Ribbon Knots Statistics of knots and entangled random walks

Reference 16

Resolution
verified exact
local_arxiv, observed 2026-08-07T10:50:55.675912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.610124Z digest=sha256:974a4a9200d7d4c2fa5212a925d67038f75711e09def0b7c8452eacdeb1728b6

Observation 3921f346-b65c-43db-9ed1-5322bdbe1196 · outbound

This paper cites Sch \"u rmann, ``On extremal finite packings,'' Discrete & Computational Geometry, vol.

Profiles of Critical Flat Ribbon Knots Sch \"u rmann, ``On extremal finite packings,'' Discrete & Computational Geometry, vol

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:50:55.812206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.613777Z digest=sha256:3516754e67581da9b6d83851f4ff0b0bca2a2cfe28364cb34bc781108b7a7716

Observation 847cfd06-466d-4aee-8a62-bb8e528409f8 · outbound

This paper cites an unresolved cited work.

Profiles of Critical Flat Ribbon Knots Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:50:55.800692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.617197Z digest=sha256:55f92f5e2928a8f648f2195d5748e317df14af22a8b441392e2303f15c4f571d

Pith citing papers

No inbound Pith citation observations are available.