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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 2026-08-08T06:32:00.761636+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

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.549009Z digest=sha256:e18479daf30a784d8b814c62c05ab6fec3743e7c44d98bb6dc0b63bcdae67ae8

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.557627Z digest=sha256:de717f911987ee9618b1450a5a5baf1d5dd7f606afb1d30a61bb2c8daa2f53fb

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.561568Z digest=sha256:f0066bab7a4a7803865356c359d765763c11b8587789647564cdd317d380de79

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.566425Z digest=sha256:b66d03800faa10bcbd9399a36ca209d1d7782dfb592c533400b19904be1bee7f

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.575516Z digest=sha256:79d5fd769636aadc1fd4fcd396701d167aeec48053ba4a2bf32dc270fca86f4b

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.580983Z digest=sha256:3f5a04593b62cad256eb8e957c9c773f4ac5329ba2f7706e7c14eec1d4cd0b53

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.584964Z digest=sha256:b3e8224d19f08583c2328db02072d65086ecfdc4be9c13898d58c20b116d5d8d

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.588638Z digest=sha256:2c8c9cce1e5ad1e75fa943c39f1080520291c7a3cee6003bd8713d1dc1b74c4e

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.592111Z digest=sha256:76bbad16f039b40dba9887449f363cb6d6536b3c8efbb9477fce60f349a9906f

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.599056Z digest=sha256:aa9b6bc4c2e5e67ef5c1f85855c8653ff83a8c3cb07db38ade34a18b429e9408

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.603151Z digest=sha256:38ac96382c153c6d7431c501151dd5f49551630eca5f3243929dea24d3586025

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.606309Z digest=sha256:4cfdc754cf1075e9089eb1ef2ad8fa2d0405fa73d8314611a3685924d321fe23

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.610124Z digest=sha256:86d5ddcbc054fe153afd22ef8a7e71be499de0c9eeae32ef1d7a789f55199c51

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.613777Z digest=sha256:46bd335eb5a57408aad5d39bd25404b196088bb3ac6d2c936fd3cf960b0664c5

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 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-08-07T10:50:55.617197Z digest=sha256:459c51948c2ebd707aab535ec94304913aea1e0a106684618d5e6e99d33c3eeb

Pith citing papers

No inbound Pith citation observations are available.