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Paper Citation Record · LEDGER

Number of Clusters in a Dataset: A Regularized K-means Approach

As of 8 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2505.22991.

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

pith.paper-citation-record.v1
2505.22991 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:04:49.908419Z

measured 40 of 40 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

40 of 40 outbound references displayed

  • verified exact3
  • verified fuzzy25
  • unresolved12
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ac6cb70e-07b4-4a01-a5a7-51435822af86 · outbound

This paper cites Ahmadian, A.

Number of Clusters in a Dataset: A Regularized K-means Approach Ahmadian, A

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:57.040194Z

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 2331970d-6861-49fb-97c6-b0a3ac560784 · outbound

This paper cites Recovering the number of clusters in data sets with noise features using feature rescaling factors.

Number of Clusters in a Dataset: A Regularized K-means Approach Recovering the number of clusters in data sets with noise features using feature rescaling factors

Reference 2

Resolution
verified exact
local_arxiv, observed 2026-08-07T13:04:50.537027Z

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 4ae7a1a0-ef0e-4e28-b508-9e4e1f1cb31f · outbound

This paper cites Anderson.

Number of Clusters in a Dataset: A Regularized K-means Approach Anderson

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:56.780620Z

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=2026-08-07T13:04:46.436227Z digest=sha256:408af79c8e8a3cc9c0e9cbcc8965f5efb6c59abc03985b3cd17d08dd9c3c40b4

Observation b85bde29-6036-4d23-9822-f94ac7dc2dde · outbound

This paper cites Arthur and S.

Number of Clusters in a Dataset: A Regularized K-means Approach Arthur and S

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:56.578366Z

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=2026-08-07T13:04:46.524886Z digest=sha256:bcbc0900e996e51d8f400d0fb8d467b5f220774082e34762ba585f207676c6f2

Observation 8676e443-3973-4c40-af0a-e71be77c6ddf · outbound

This paper cites Bachem, M.

Number of Clusters in a Dataset: A Regularized K-means Approach Bachem, M

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:56.383246Z

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=2026-08-07T13:04:46.605511Z digest=sha256:ac9cedbe6e1cdf93ac1966e1903e58c3d040eb64dca9e0968a8cf060fbc0e161

Observation e37c3b49-59a6-45d3-8b3e-1938a4defbf9 · outbound

This paper cites Recombinator-k-means: An evolutionary algorithm that exploits k-means++ for recombination.

Number of Clusters in a Dataset: A Regularized K-means Approach Recombinator-k-means: An evolutionary algorithm that exploits k-means++ for recombination

Reference 6

Resolution
verified exact
local_arxiv, observed 2026-08-07T13:04:50.343281Z

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 b781a6e6-24c5-48a8-960a-618d178b1afe · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:56.204151Z

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=2026-08-07T13:04:46.766720Z digest=sha256:e5d51d164f1eb7db0a67a234e92d8f5831f4470afa69394a27b6738c699d40cf

Observation 9c8cccc1-6ac7-4b9a-9ae1-1ceb6f6cafaf · outbound

This paper cites Bozdogan.

Number of Clusters in a Dataset: A Regularized K-means Approach Bozdogan

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:56.045127Z

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=2026-08-07T13:04:46.850708Z digest=sha256:a0ab48b45253a86d758348c88803388935d5534c10096341676ef4031e3f8ba5

Observation e2d0a4eb-d8b1-422c-81cc-94935036b515 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:55.909023Z

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=2026-08-07T13:04:46.950897Z digest=sha256:b44288f3be0123e66657b2185437e4e41423d131f9f0fab7f3244c32fed01de9

Observation 37ebfc11-1248-415d-89a3-416630563a27 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:55.749909Z

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 8e14bf0f-b22b-4d4b-bf02-e4fe8be5a365 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:55.610450Z

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 89e101c3-810e-4604-a668-773cb0faf63c · outbound

This paper cites Frank and A.

Number of Clusters in a Dataset: A Regularized K-means Approach Frank and A

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:55.449685Z

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=2026-08-07T13:04:47.176034Z digest=sha256:cc09f8cc75b70463cd4bd5da53a36de6bbe44590962265823379f1de2d40d6ca

Observation f51c542e-fa1a-43d9-abb3-c6bc5dbf752a · outbound

This paper cites Franti and S.

Number of Clusters in a Dataset: A Regularized K-means Approach Franti and S

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:55.341184Z

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=2026-08-07T13:04:47.306298Z digest=sha256:c30b3d9e8b2fa8d9321795431567ef5848d9bd0ed7fbf86655e13ca41d752fbe

Observation af31801a-022b-4e70-95b4-2ada1605414e · outbound

This paper cites Estimating the number of clusters using cross-validation.

Number of Clusters in a Dataset: A Regularized K-means Approach Estimating the number of clusters using cross-validation

Reference 14

Resolution
verified exact
local_arxiv, observed 2026-08-07T13:04:50.166207Z

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=2026-08-07T13:04:47.375125Z digest=sha256:41829ea30aebdce5d532544ab279fc463fef868020a2040dab530fd2213ab55d

Observation 7781a075-326e-4b6f-9b1e-0eba3f421b2d · outbound

This paper cites Fujita, D.Y.

Number of Clusters in a Dataset: A Regularized K-means Approach Fujita, D.Y

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:55.201123Z

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=2026-08-07T13:04:47.447948Z digest=sha256:5181dd480c84672290959c71ddb1b2a098d6dcf3aa41d81e096c1f7d395eb413

Observation 54f94ea9-1b68-4183-af6f-5ab531ac2a38 · outbound

This paper cites Gersho and R.M.

Number of Clusters in a Dataset: A Regularized K-means Approach Gersho and R.M

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:54.916750Z

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=2026-08-07T13:04:47.544276Z digest=sha256:927c6dc033b2fd2cb58bd736a92a1c81d2cad41217adf3c55155e29dabc7e51e

Observation 83c4920e-0a62-4bf2-89a3-cbd58bb09ffd · outbound

This paper cites Gradshteyn and I.M.

Number of Clusters in a Dataset: A Regularized K-means Approach Gradshteyn and I.M

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:54.623552Z

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=2026-08-07T13:04:47.629266Z digest=sha256:c060ef12173abefe5e56410e1b38aeda7bd2002df682ac0f26791a005aaad71c

Observation bb90cbb5-6ec5-43a9-9bdd-9b0b85cbef69 · outbound

This paper cites Jain and R.C.

Number of Clusters in a Dataset: A Regularized K-means Approach Jain and R.C

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:54.397606Z

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=2026-08-07T13:04:47.709706Z digest=sha256:f3a26d20a1a383a67eb4623499d7bf5ab8d73cae6f3e2239a079f69abad60845

Observation 6dc91853-8d6a-403c-9640-caa4e1be9fb4 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:54.253593Z

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=2026-08-07T13:04:47.823525Z digest=sha256:5cc395c63c85feb1215cd9e1462597e53137a4d4531d9f4b447a94f7835c442b

Observation b67a5435-0600-45cc-918a-1f3a2ed54411 · outbound

This paper cites Kamgar-Parsi, J.A.

Number of Clusters in a Dataset: A Regularized K-means Approach Kamgar-Parsi, J.A

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:54.081866Z

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 976491ad-9bb2-4c9c-ba14-438e6597f885 · outbound

This paper cites Kamgar-Parsi and B.

Number of Clusters in a Dataset: A Regularized K-means Approach Kamgar-Parsi and B

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:53.939115Z

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 390b87ee-6de7-4a71-acc1-d84f43c7e40b · outbound

This paper cites Kamgar-Parsi and B.

Number of Clusters in a Dataset: A Regularized K-means Approach Kamgar-Parsi and B

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:53.774354Z

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 9c929101-eacb-42a2-ad4f-48097213f8e1 · outbound

This paper cites Kanungo, D.M.

Number of Clusters in a Dataset: A Regularized K-means Approach Kanungo, D.M

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:53.594233Z

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=2026-08-07T13:04:48.240414Z digest=sha256:ff5b666373d8a9b4969ff49fdc43cfce13ecd8b050453b18977ef74de9c599f7

Observation 1c74d2cb-b5d3-4836-839a-40d059e3b552 · outbound

This paper cites Krzanowski and Y .T.

Number of Clusters in a Dataset: A Regularized K-means Approach Krzanowski and Y .T

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:53.446122Z

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=2026-08-07T13:04:48.336835Z digest=sha256:1c8622c8e5adf0f15605f6f4be6cf0b4efcb3698586d6ac2d8f4f9d178c6dc16

Observation 41a943df-8e10-4e75-b813-3cb92d5e3689 · outbound

This paper cites Kulis and M.I.

Number of Clusters in a Dataset: A Regularized K-means Approach Kulis and M.I

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:53.279488Z

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=2026-08-07T13:04:48.426491Z digest=sha256:7ce74f86bfebaba9a20bb317fb3aad8e4f8e96b62eaea9b92a5944e4e2ebc6cf

Observation 904b4134-c232-4cf7-980a-fbd3f394cf57 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:53.135386Z

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 16ea8d4a-8334-4245-8ab2-e26b9d0fbcd5 · outbound

This paper cites Linde, A.

Number of Clusters in a Dataset: A Regularized K-means Approach Linde, A

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:52.982499Z

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 bf11d1d8-6875-4ab8-900f-e17e4ce6c713 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:52.808925Z

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 f978c8cc-16d5-4788-ae8a-39530d4d149a · outbound

This paper cites Manning, P.

Number of Clusters in a Dataset: A Regularized K-means Approach Manning, P

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:52.609981Z

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 c55e8309-7a0f-40ff-9808-95bb437d26fd · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:52.398137Z

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=2026-08-07T13:04:48.861199Z digest=sha256:a35c07d7d48d9c7090e80e174fa410eef1f616722b02220253bad8af7b7e0f26

Observation d1673e53-8254-4e59-bb55-2a5ba42ef029 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:52.199872Z

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=2026-08-07T13:04:48.996040Z digest=sha256:90e481164721a6ea7e7b1f3f44737ed62864475df13d28d6d8154e1cf896f9fa

Observation b8ad7e33-ac5d-4ff3-831d-cc6efc3dfd3f · outbound

This paper cites Rousseeuw.

Number of Clusters in a Dataset: A Regularized K-means Approach Rousseeuw

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:52.062568Z

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=2026-08-07T13:04:49.110768Z digest=sha256:6a578907a1e324f696015a8f33579deea7e0e66ec1ed2f558b5803f80fccc2d6

Observation 4258a392-3b4e-416f-812c-aa496985d357 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:51.877418Z

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=2026-08-07T13:04:49.174032Z digest=sha256:8a452601ccf48f13d5b98f406f5321c6b3cff2d7c9efbc7e2250b30304708e4c

Observation 123cae2c-1753-465b-8cf7-ee960fd47608 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:51.704890Z

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=2026-08-07T13:04:49.280298Z digest=sha256:279aba22b03ad380ecd0a958d8bc0f80fdff2f99feb3b40ff77d372b77625a4f

Observation acb9d018-5573-443d-b527-62dcc1a8a65c · outbound

This paper cites Sugar and G.M.

Number of Clusters in a Dataset: A Regularized K-means Approach Sugar and G.M

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:51.529523Z

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=2026-08-07T13:04:49.395973Z digest=sha256:82923da086d2532cd7e3193e9f7d8c80fa97e72c98bc3442c1efe08752b01f53

Observation 81bad8a1-c601-4d40-9f8f-b1cb21f1407b · outbound

This paper cites Szczypi´nski, M.

Number of Clusters in a Dataset: A Regularized K-means Approach Szczypi´nski, M

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:51.380172Z

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=2026-08-07T13:04:49.475300Z digest=sha256:b557f621fecb410d539a52f01ff3c22906970d899f005019a329bcb3d4e2242a

Observation 3121c814-4aeb-43b3-a5f1-75d44b1d3534 · outbound

This paper cites Tibshirani, G.

Number of Clusters in a Dataset: A Regularized K-means Approach Tibshirani, G

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:51.179870Z

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=2026-08-07T13:04:49.585977Z digest=sha256:505f020f2e9c16bee40afeabeebad8726f4f72c1283fe029ba0e3abdcca17dfc

Observation e83ff1ef-e072-49e8-8893-5ab57b22eb48 · outbound

This paper cites Vidal, Y.

Number of Clusters in a Dataset: A Regularized K-means Approach Vidal, Y

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:51.016328Z

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=2026-08-07T13:04:49.667631Z digest=sha256:6913191033729c2a75481c9c6b5f55ca924132915d941a426b5b010135dd76ba

Observation 2516949b-7000-449e-a9d0-06848c811e98 · outbound

This paper cites an unresolved cited work.

Number of Clusters in a Dataset: A Regularized K-means Approach Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-07T13:04:50.881453Z

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=2026-08-07T13:04:49.758918Z digest=sha256:65f8b3c14fb813fec6a0521366832114fc209fa59d55bd7a558327dfef289880

Observation 99b44445-a15a-49a1-afd5-3a46ca1bcb53 · outbound

This paper cites (A-4) With repeated use of (A-3), Eq.

Number of Clusters in a Dataset: A Regularized K-means Approach (A-4) With repeated use of (A-3), Eq

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T13:04:50.708599Z

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=2026-08-07T13:04:49.908419Z digest=sha256:dc1b0b31950335689ba7eb39a97fe7517e8d602dfbbb60610525029ff9ad6d94

Pith citing papers

No inbound Pith citation observations are available.