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Paper Citation Record · LEDGER

Partial Deranged Bell Numbers and Their Combinatorial Properties

As of 8 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 4 inbound Pith citation observations for arXiv:2507.21643.

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

pith.paper-citation-record.v1
2507.21643 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:45:02.467480Z

measured 35 of 35 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 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T14:44:45.383765Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-03T21:58:58.486581Z

Reference resolution

31 of 31 outbound references displayed

  • verified exact0
  • verified fuzzy18
  • unresolved11
  • parse uncertain0
  • malformed identifier2
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e7c7b476-f886-401b-88da-2b2fc6e22974 · outbound

This paper cites Acu, J.A.

Partial Deranged Bell Numbers and Their Combinatorial Properties Acu, J.A

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:03.137334Z

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=pdf_text observed=2026-08-06T12:45:00.168473Z digest=sha256:47a45c980815e29098c2e1274072f603ef9985193ee412f8a0ec31dd0127c43f

Observation 81fb31fc-6ecd-4cc7-a52b-812bfb077fa6 · outbound

This paper cites Adell and S.

Partial Deranged Bell Numbers and Their Combinatorial Properties Adell and S

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:03.117049Z

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=pdf_text observed=2026-08-06T12:45:00.238371Z digest=sha256:171e8620f8be8ccbc364b951248e0a4537f72a2d6ff6073d72de39e7d86cb565

Observation 27844c0d-bb25-4cf1-9786-73eb43973615 · outbound

This paper cites Belbachir and Y.

Partial Deranged Bell Numbers and Their Combinatorial Properties Belbachir and Y

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:03.098325Z

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=pdf_text observed=2026-08-06T12:45:00.298244Z digest=sha256:53b980e6ec5bc39c63f5d86a1d3e4c0a00b55fdbf7ba6fd7d070d7b599812142

Observation b2d6da7b-bdf3-4f5b-86c7-2033cdc84879 · outbound

This paper cites Belbachir, Y.

Partial Deranged Bell Numbers and Their Combinatorial Properties Belbachir, Y

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:03.080994Z

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=pdf_text observed=2026-08-06T12:45:00.394579Z digest=sha256:5d713b8b4aea9765c3616309a44f15cf0d50a5cb5d0d27eb5394d2904cc48342

Observation 2cad090d-9807-47d8-851e-cdec87c419a2 · outbound

This paper cites an unresolved cited work.

Partial Deranged Bell Numbers and Their Combinatorial Properties Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:45:03.060421Z

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=pdf_text observed=2026-08-06T12:45:00.499329Z digest=sha256:f9a65dc9f75aeae684a63c227af90c051c1d92775ebca0c030fc274b6486fb00

Observation 4d5b8a9f-3d7c-402b-8773-f5800b2a32fd · outbound

This paper cites an unresolved cited work.

Partial Deranged Bell Numbers and Their Combinatorial Properties Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:45:03.041985Z

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=pdf_text observed=2026-08-06T12:45:00.566423Z digest=sha256:895ba88dcabd4fac9915670c56e7a4687b7598fc4931664961819e8caecbb19f

Observation 8fd459f5-4cb6-4dbc-86f9-df30793e5abb · outbound

This paper cites an unresolved cited work.

Partial Deranged Bell Numbers and Their Combinatorial Properties Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:45:03.024718Z

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=pdf_text observed=2026-08-06T12:45:00.632150Z digest=sha256:7c12a6ac3a85d0fbf3037098b416b67897ad2f4cfbb5e7fb4b360dae3fbec91c

Observation ff2e816b-70bc-4793-a192-b30b9f413717 · outbound

This paper cites an unresolved cited work.

Partial Deranged Bell Numbers and Their Combinatorial Properties Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:45:02.997902Z

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=pdf_text observed=2026-08-06T12:45:00.688122Z digest=sha256:3a9fb9ea8eee38cb15d60d0425c1a6924fdbf1f8c4313ba636bb7364c8294555

Observation ecb11ee0-6622-485f-b1d1-bd87efe56041 · outbound

This paper cites De Angelis and D.

Partial Deranged Bell Numbers and Their Combinatorial Properties De Angelis and D

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.979918Z

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=pdf_text observed=2026-08-06T12:45:00.747338Z digest=sha256:ca4dc7f5f2bf1569bf062b8bb7e4e6b08959cca6c38ccf7fd49233ce3aa9d6d8

Observation 6157f2e1-977c-42f4-a42a-c4796f8b664b · outbound

This paper cites Dil and V.

Partial Deranged Bell Numbers and Their Combinatorial Properties Dil and V

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.950973Z

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=pdf_text observed=2026-08-06T12:45:00.818127Z digest=sha256:07829c80425a29b22dc720e3e00dc43f4c1008587936da71c8f079e9bf697e30

Observation 5a60fb62-8cd3-4fa6-a991-5048d05ff0ec · outbound

This paper cites Dil and V.

Partial Deranged Bell Numbers and Their Combinatorial Properties Dil and V

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.935141Z

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=pdf_text observed=2026-08-06T12:45:00.891024Z digest=sha256:5694dc341f142caae73604a24f4b8bdfd04b523e0dd2b6e45f14db9aa6ed9813

Observation 759b4d22-1afc-4d4c-be7a-cae7f71bcb66 · outbound

This paper cites Dil and V.

Partial Deranged Bell Numbers and Their Combinatorial Properties Dil and V

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.919344Z

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=pdf_text observed=2026-08-06T12:45:00.976215Z digest=sha256:87b4897622dfe398cda974d2a76c0694b90019ae863e1924b91c108955d8da83

Observation 2a0942eb-cb5d-4a91-b16e-71094862a1ad · outbound

This paper cites Dobi˜ nski, Summierung der Reihe P nm/n! f¨ urm = 1 , 2, 3, 4, 5,.

Partial Deranged Bell Numbers and Their Combinatorial Properties Dobi˜ nski, Summierung der Reihe P nm/n! f¨ urm = 1 , 2, 3, 4, 5,

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.904156Z

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=pdf_text observed=2026-08-06T12:45:01.053006Z digest=sha256:0f023929f841befa4fa531d128dcd4991509edbaac57ba215861481f9f223111

Observation 82d4a1f8-d05f-4415-aeb4-2ce6bbe9677a · outbound

This paper cites Freud and P.M.

Partial Deranged Bell Numbers and Their Combinatorial Properties Freud and P.M

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.884090Z

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=pdf_text observed=2026-08-06T12:45:01.117729Z digest=sha256:6e7949bf67d442c640fd0013fd5e15b1090bb0470ea0929f131673ea54295ed5

Observation 4843f8eb-9aa3-474e-99fc-6004f9eda935 · outbound

This paper cites an unresolved cited work.

Partial Deranged Bell Numbers and Their Combinatorial Properties Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:45:02.867650Z

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=pdf_text observed=2026-08-06T12:45:01.216187Z digest=sha256:def9b33764814ba52b338b7a45625dbc2dce590b616c91ec5bba802955ff9af4

Observation 5706ad64-3ea2-478c-9f8f-21fda27cf330 · outbound

This paper cites an unresolved cited work.

Partial Deranged Bell Numbers and Their Combinatorial Properties Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:45:02.851323Z

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=pdf_text observed=2026-08-06T12:45:01.282206Z digest=sha256:3ac853ce73771959ebf38137f953db411823b857dd7915010da37e19aa7e1912

Observation bafc3b27-787f-441d-967d-99b12987a1d0 · outbound

This paper cites Kargın, Some formulae for products of geometric polynomials with ap- plications, J.

Partial Deranged Bell Numbers and Their Combinatorial Properties Kargın, Some formulae for products of geometric polynomials with ap- plications, J

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.831804Z

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=pdf_text observed=2026-08-06T12:45:01.320941Z digest=sha256:60bbb9c00949ba61b569b2af4708352ab57510beaaf11b5debd06f39ab1847c9

Observation c67570ea-0d83-4cd5-9ffa-8296b597c2f6 · outbound

This paper cites Kargın and E.

Partial Deranged Bell Numbers and Their Combinatorial Properties Kargın and E

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.811846Z

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=pdf_text observed=2026-08-06T12:45:01.334044Z digest=sha256:b26dc0885456d46a58383c6b4f6a379f4df5a704e40c0169f0d43ddca0a71cd8

Observation 8cec5b05-be79-4b39-8665-ed924fe8c575 · outbound

This paper cites Kargın and R.

Partial Deranged Bell Numbers and Their Combinatorial Properties Kargın and R

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.792995Z

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=pdf_text observed=2026-08-06T12:45:01.419554Z digest=sha256:5c29273877053cf74c43d37e383af8b6dc045fe29ed62828dae18868ba128d6c

Observation 2ab218f5-8db8-474c-8361-40e1e7b2f4ae · outbound

This paper cites Kargın and B.

Partial Deranged Bell Numbers and Their Combinatorial Properties Kargın and B

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.776207Z

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=pdf_text observed=2026-08-06T12:45:01.572040Z digest=sha256:9e80626123deb3739ab40cfdab482e468d2cd23b0307402b7783f626f6a8a6f1

Observation 9b44472b-653d-4bb2-a8a0-a14cf4809533 · outbound

This paper cites an unresolved cited work.

Partial Deranged Bell Numbers and Their Combinatorial Properties Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:45:02.759418Z

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=pdf_text observed=2026-08-06T12:45:01.738503Z digest=sha256:5b696204b7733def913449461843f1d47c06edef9b96ec5b961a9dbacb2c14a2

Observation d7b0ad15-171c-478d-83b7-217061599a5f · outbound

This paper cites Mez˝ o, Ther-Bell numbers, J.

Partial Deranged Bell Numbers and Their Combinatorial Properties Mez˝ o, Ther-Bell numbers, J

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.738947Z

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=pdf_text observed=2026-08-06T12:45:01.864049Z digest=sha256:ae50e155def51d7d86354815e00f95b24702071248f186af60cf040d951c9a0a

Observation 53f0b3b2-dd1d-411b-bd7a-9a1fd2fbb92c · outbound

This paper cites Mihoubi and H.

Partial Deranged Bell Numbers and Their Combinatorial Properties Mihoubi and H

Reference 23

Resolution
malformed identifier
raw_fallback, observed 2026-08-06T12:45:02.720853Z

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=pdf_text observed=2026-08-06T12:45:02.011077Z digest=sha256:10af62f3b7ca87f978f8828676b18ae59e172ba7634170767a6dde04fc25fc00

Observation 7f382286-a21c-4be7-9b6e-dd4ea804c862 · outbound

This paper cites an unresolved cited work.

Partial Deranged Bell Numbers and Their Combinatorial Properties Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:45:02.703291Z

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=pdf_text observed=2026-08-06T12:45:02.134513Z digest=sha256:a6befc35885054af118ca43a79c9e1531be6efa7a720871c116424b812d81c73

Observation b35ddaab-d320-40ad-ab5b-9a920ccf409b · outbound

This paper cites Moshtagh and R.

Partial Deranged Bell Numbers and Their Combinatorial Properties Moshtagh and R

Reference 25

Resolution
malformed identifier
doi_truncated, observed 2026-08-06T12:45:02.536421Z

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=pdf_text observed=2026-08-06T12:45:02.281140Z digest=sha256:a0fa4af3cf24b09d1b51d87acc4682ee12eaca5d8c32075b2ac601d76d27fc25

Observation 7ad42368-11d3-45d3-8054-84dc598533c3 · outbound

This paper cites Nkonkobe, B.

Partial Deranged Bell Numbers and Their Combinatorial Properties Nkonkobe, B

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.678784Z

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=pdf_text observed=2026-08-06T12:45:02.434425Z digest=sha256:056fb42b8da296502b2b71af28ccecf56bb81959cb7d8e0649168d3108cec1d6

Observation 3a9533c7-1b5d-4dfc-a2bd-22fc688bf412 · outbound

This paper cites an unresolved cited work.

Partial Deranged Bell Numbers and Their Combinatorial Properties Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:45:02.656784Z

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=pdf_text observed=2026-08-06T12:45:02.440624Z digest=sha256:5d0b102bc258cdc35ab42ad255f06f9af452b7a047e071be52da1c05d20938aa

Observation 6ad0149b-5a31-4cf2-877a-7cd61eea9d86 · outbound

This paper cites Quaintance and H.

Partial Deranged Bell Numbers and Their Combinatorial Properties Quaintance and H

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.633608Z

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=pdf_text observed=2026-08-06T12:45:02.448204Z digest=sha256:c0a0d26dc1ccde155a31129d7c7e7ab9dc7be80f69fd59b35fb2db3cfbf54643

Observation f2d0f413-cae9-4bfc-aed4-234a74d9d0fe · outbound

This paper cites Riordan, An Introduction to Combinatorial Analysis , Princeton Univer- sity Press, Princeton, NJ, 1978.

Partial Deranged Bell Numbers and Their Combinatorial Properties Riordan, An Introduction to Combinatorial Analysis , Princeton Univer- sity Press, Princeton, NJ, 1978

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:45:02.609246Z

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=pdf_text observed=2026-08-06T12:45:02.455289Z digest=sha256:45cfbc8a72f24e92cda803a2c9c9ba1a92484d8ebb059a36e246a854269f9b9f

Observation d90dff72-39fa-4c8e-96e7-6f203c595a76 · outbound

This paper cites an unresolved cited work.

Partial Deranged Bell Numbers and Their Combinatorial Properties Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:45:02.581837Z

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=pdf_text observed=2026-08-06T12:45:02.460703Z digest=sha256:b83ae7c32acd7c437c5085a470f44b4164418734fb393050b0d347ff933d8191

Observation 3eb6894e-7651-4fbd-83e2-46ddb2444b86 · outbound

This paper cites an unresolved cited work.

Partial Deranged Bell Numbers and Their Combinatorial Properties Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-06T12:45:02.564141Z

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=pdf_text observed=2026-08-06T12:45:02.467480Z digest=sha256:e27449ab5c8e108f1c814cf728059743dc540ee49497bdc9f0909b187a9e9a5f

Pith citing papers

Observation 12e26fdb-c881-44e5-82d3-94133d607dea · inbound

Combinatorics of higher order degenerate $r$-DERANGED Bell Numbers cites this paper.

Combinatorics of higher order degenerate $r$-DERANGED Bell Numbers Partial Deranged Bell Numbers and Their Combinatorial Properties

Reference 14

Resolution
verified exact
arxiv_id, observed 2026-05-12T00:51:14.862953Z

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=pdf_text observed=2026-05-12T00:50:29.420224Z digest=sha256:0b4742899e10d44be6cbbdd572e8c4f291c89811aa901eada965602c418776fa

Observation 99b6798e-1364-4264-b5bc-7c705d350567 · inbound

Combinatorics of higher order degenerate $r$-DERANGED Bell Numbers cites this paper.

Combinatorics of higher order degenerate $r$-DERANGED Bell Numbers Partial Deranged Bell Numbers and Their Combinatorial Properties

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-02T14:44:45.383765Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-02T14:44:45.383765Z digest=sha256:8cb0ec2a1a44420a71b3267a88fb17b0220f4de30f5fc534ac3c9f3623ca383e

Observation 73cf6816-c502-4575-bc02-83188fb2784a · inbound

On Deranged Unit-Interval Parking Functions and the Deranged Bell Numbers cites this paper.

On Deranged Unit-Interval Parking Functions and the Deranged Bell Numbers Partial Deranged Bell Numbers and Their Combinatorial Properties

Reference 6

Resolution
verified exact
arxiv_id, observed 2026-07-03T21:58:58.488067Z

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=pdf_text observed=2026-07-03T21:51:48.776220Z digest=sha256:a81c2d846fe9125bbcd7446455122918a2f08924c009165ec483bf22f0a35c21

Observation aac25aba-2f96-4fb1-b03b-49930715b67d · inbound

On Deranged Unit-Interval Parking Functions and the Deranged Bell Numbers cites this paper.

On Deranged Unit-Interval Parking Functions and the Deranged Bell Numbers Partial Deranged Bell Numbers and Their Combinatorial Properties

Reference 7

Resolution
unresolved
no resolver link, observed 2026-07-12T09:41:41.050212Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-12T09:41:41.050212Z digest=sha256:48111e3ba70df56e87948669daa24ab2e0de8b7be9868ded290de027a9cda533