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Paper Citation Record · LEDGER

Numerical approximation of bi-harmonic wave maps into spheres

As of 7 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2409.11366.

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

pith.paper-citation-record.v1
2409.11366 v2

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-23T20:28:09.149943Z

measured 19 of 19 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

19 of 19 outbound references displayed

  • verified exact0
  • verified fuzzy10
  • unresolved9
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0ff15607-0831-41b8-b22c-0a576fabfa14 · outbound

This paper cites an unresolved cited work.

Numerical approximation of bi-harmonic wave maps into spheres Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-05-23T20:28:24.876496Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:a5dd997d808150e1abd7249f1e5ddded2bebbaa9f98c08833de2e941a6802f86

Observation 6db0bd47-3f24-4387-9a15-b1c76d79f65c · outbound

This paper cites an unresolved cited work.

Numerical approximation of bi-harmonic wave maps into spheres Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-05-23T20:28:24.879501Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:7ab423cd7dd8c6769f72660e19e6ebaedac93c81eb6055808515db6dcae13f02

Observation ea30a6ea-6bd9-4c54-a4e7-c38e551b3e7d · outbound

This paper cites an unresolved cited work.

Numerical approximation of bi-harmonic wave maps into spheres Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-05-23T20:28:24.882573Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:df85751e8c55016cc2e55bd33235f7d4a08c86d111861b3b014ebc32bdb91d31

Observation e9b009ae-39cf-48d9-bbea-f85a8b6eb45f · outbound

This paper cites Bartels.Numerical approximation of partial differential equations, volume 64 ofTexts in Applied Mathematics.

Numerical approximation of bi-harmonic wave maps into spheres Bartels.Numerical approximation of partial differential equations, volume 64 ofTexts in Applied Mathematics

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T20:28:24.873334Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:b62c5b7a477fd28b1035f6bbb51c51d8c6a04dcb9ee20cd30f461dd4ed075db3

Observation 6dbb78ed-224c-46f8-b991-7c983448b6cc · outbound

This paper cites an unresolved cited work.

Numerical approximation of bi-harmonic wave maps into spheres Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-05-23T20:28:24.866234Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:9328081e3a7fa8a949dfda28012d6d0d813d6a5e0ce98b38ebad98165a04c3d0

Observation 22624a73-e97f-467d-adf0-652b07375fb1 · outbound

This paper cites Bartels, X.

Numerical approximation of bi-harmonic wave maps into spheres Bartels, X

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T20:28:24.869583Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:ef560b66f0c6635066936b59d2c7d130bd52f9aa407d98f22689c7abe70676e3

Observation a63730b4-c557-4871-8809-8e8543fbe5e1 · outbound

This paper cites Bartels, C.

Numerical approximation of bi-harmonic wave maps into spheres Bartels, C

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T20:28:24.888644Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:7e12b49add9c9eed83bb8f364bf3e32533f18316f2f87fcce9bc68351a046542

Observation dfaf3a00-8b61-4cab-b4e0-432f2463f646 · outbound

This paper cites Baňas, Z.

Numerical approximation of bi-harmonic wave maps into spheres Baňas, Z

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T20:28:24.885590Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:0c1904daf71442437cad06cad76a9ec2b250f2cbbe5e4d53f040632a5441dda5

Observation 9dada106-a76e-44b1-aa65-18646aabd93a · outbound

This paper cites Baňas, Z.

Numerical approximation of bi-harmonic wave maps into spheres Baňas, Z

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T20:28:24.891993Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:48a50acb6a548c52af52981ee59a11f6bc762d4d0fd6d766a7077aab16f61c05

Observation 61bbb299-400b-4251-94ca-2149eab08416 · outbound

This paper cites Baňas, A.

Numerical approximation of bi-harmonic wave maps into spheres Baňas, A

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T20:28:24.913548Z

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.

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Observation 765ef081-15e2-472a-a3c3-761af86abf94 · outbound

This paper cites an unresolved cited work.

Numerical approximation of bi-harmonic wave maps into spheres Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-05-23T20:28:24.897429Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:c8522beb1948f5266c2696474f20175751172ae9876cf9cba88a34b57dd56e8b

Observation a2d8c6c7-3d77-4e4a-a1ab-fb96afbeb74d · outbound

This paper cites an unresolved cited work.

Numerical approximation of bi-harmonic wave maps into spheres Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-05-23T20:28:24.932516Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:73067976fb27d15e552312157ef39d84a72555f6b04f0114b3d15bbc0f07cf99

Observation 068ff615-e824-405f-9989-0cb948712f6b · outbound

This paper cites Eymard, R.

Numerical approximation of bi-harmonic wave maps into spheres Eymard, R

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T20:28:24.925062Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:87fe713f0ac126563f7759f23b55da6b558497e1f8a21d62a327135961257ec0

Observation 0c78a39c-0fca-4c0e-8b29-1c3dd3c6634a · outbound

This paper cites an unresolved cited work.

Numerical approximation of bi-harmonic wave maps into spheres Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-05-23T20:28:24.921402Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:12a555cfd209ccfd1557bbf9ec42d5c8ddb65ac186cae5b7ad5b45f01a4f3e08

Observation fd640010-72fc-4911-aca4-b1f523848924 · outbound

This paper cites an unresolved cited work.

Numerical approximation of bi-harmonic wave maps into spheres Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-05-23T20:28:24.917658Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:3510a0571ec8bbe50a07501143029f8374f54ad91446d2ff701cc1ae83bcf471

Observation 36954604-e4d1-44a9-a9ac-7ab6e4ecb8e3 · outbound

This paper cites an unresolved cited work.

Numerical approximation of bi-harmonic wave maps into spheres Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-05-23T20:28:24.906158Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:eec4ff62beef8dfcd86e7239722d0fb105eadd98d8080619ed143a17b819a157

Observation c66e36b3-173b-4120-ab58-e7816755dee1 · outbound

This paper cites Porrmann.

Numerical approximation of bi-harmonic wave maps into spheres Porrmann

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T20:28:24.928718Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:1d16c29a1b82e32a6b7bfa93b9f142fc2080909af11e991205ad4338fe880b0e

Observation 83ed46a9-e886-4b58-b2d2-b3d8cd9a317b · outbound

This paper cites Energy bounds for a fourth-order equation in low dimensions related to wave maps.Proc.

Numerical approximation of bi-harmonic wave maps into spheres Energy bounds for a fourth-order equation in low dimensions related to wave maps.Proc

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T20:28:24.902072Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:9619780c8a505a430cd812cb2bbf87dc1c5913f8e3418e0526105b2ba074f326

Observation 7172fd82-7f73-46b4-8968-16c717d517f1 · outbound

This paper cites Temam.Navier-Stokes equations.

Numerical approximation of bi-harmonic wave maps into spheres Temam.Navier-Stokes equations

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T20:28:24.909965Z

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=pdf_text observed=2026-05-23T20:28:09.149943Z digest=sha256:29669aeb57d0ce96749e250572ecedeceb91619aedc803dc93883e75f4853da8

Pith citing papers

No inbound Pith citation observations are available.