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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 2026-08-07T06:34:17.273281+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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.168473Z digest=sha256:565a9c45e89726ed17cb01a1763675aa4321b78dfc6d30445220b128ca60000a

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.238371Z digest=sha256:c5f9f78e31e5a92d27013f88f9679cfa7da32983891a23cbbd0972b671eaac24

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.298244Z digest=sha256:e928691aa29f85e1c1a03ffed8f11fbc3c775fa48019d34530acac2a349b4a68

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.394579Z digest=sha256:efd06693b26121a17f81816eb864b97c5c6264b9511f214f98263aef4b7cb2fc

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.499329Z digest=sha256:ada294f9c58730ef600ab6e880dac33de017c4d0a2f0f180317dede74a6f3f96

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.566423Z digest=sha256:ec2d577e87d2affd11b040b5d9e1dd7ca36bfc11595df7dc3d6e6f75e586b750

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.632150Z digest=sha256:414ee1e95b950b5af9a4e47cc45b6bf665dbedac5d0880090ae607845ad10421

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.688122Z digest=sha256:54c218748b5fa2c206b31c3ed8a8651a9cf6e7df58c9bcd2340272dc8140ab84

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.747338Z digest=sha256:520f692e377e8e58b4a951b44e0c351e8988924da1e71148a4f11e099b243369

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.818127Z digest=sha256:ce28e725b3d78e6334b509e68d99dfc9acdf2967dc40ddd042d1f2fbcc831fe8

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.891024Z digest=sha256:f0bb7e445f05239dd5d6f13a9d5925903ec7a58d7339f307e3eceefdf2c6f987

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:00.976215Z digest=sha256:9b3fce458ad19a3fea30c8299a87fa384a9ae8da7c3031184624b149a78dd265

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:01.053006Z digest=sha256:476d115e8f3a3fd99718124e57b700447e8a8b729e4740f76a4d113a15e4051d

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:01.117729Z digest=sha256:7b0463be1406574c8e9b7568d194207441bca12a9b27721f4c79657400fff518

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:01.216187Z digest=sha256:56e0ba5412955d2c7cef169d52422589d909519bb1aa00ac8fe7fc549e7082f8

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:01.282206Z digest=sha256:d54bf844c743f410b4c95021162b389feb0ecbb92d2088d24542d72ca619e9d4

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:01.320941Z digest=sha256:756d68a7b538ddd10e60547dc31d03659c98e153f06617363c493f126ba20b58

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:01.334044Z digest=sha256:f896235f074964ae28e29b5e9da8e5b6d7ee902c65308eb6be02b0a391750796

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:01.419554Z digest=sha256:a821b84ca549bb095b9a6845d41152480a4a6341ff1d937763f4876ab5179b83

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:01.572040Z digest=sha256:49b40c2dd255c993c0f5a3b6aad399ecb07526db05a8352977adbb86e50db212

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:01.738503Z digest=sha256:e36b97cc52a598a2d11b664b90474dbace6c49f5e1a8a77c6a5cea20e1e6d77e

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:01.864049Z digest=sha256:fb43ed157b64c59fcdee5d2a430a8af47f267ee860b8bc952c4acbb4e2e4e464

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:02.011077Z digest=sha256:e2c7a0f38f1880e9f5fc4dc8f68ea5818c8690b6dfaab8f8bc1f2f1b58a58803

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:02.134513Z digest=sha256:2f8a8d09461fbf00841669172b6c8b61e2ae4befda70019c4b97918a6acc5070

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:02.281140Z digest=sha256:a80f5407639a1a866b08f3366c8317fc263693f9deab65cbee66f2fbad9bf9b9

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:02.434425Z digest=sha256:a7ffe7597ff1c62b1da5bd93130ad51f663ee0a665c08b14134389ac4121c1d6

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:02.440624Z digest=sha256:91a84d30a031d33e01edebccdbd84053ba62f82853a7bc65ed72a410bb91d61d

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:02.448204Z digest=sha256:f6c96490ef7a5557a63fa7d5dbea73e26342587ad60d8375a9736b4b5e25ef07

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:02.455289Z digest=sha256:f78e8ab08bc747050bdfa73df8d4a003b5f44e0ae7cf52f1f6590179fa54831b

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:02.460703Z digest=sha256:556f2924f834c840bd6aba39723f6f50987ccee49788ee372d22126b7c5277fa

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-08-06T12:45:02.467480Z digest=sha256:5995eb82e5db4624b03ce2e3acd327246d7b912d72e6be6ea57adc61da35ad09

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-12T00:50:29.420224Z digest=sha256:1c3a08f6d3c6e47d14a072b5f11308a6ac1f3f1867fd971bdd8e03b1ab1111f7

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 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-07-03T21:51:48.776220Z digest=sha256:48c7ba6299d2da81f1d76a0b9debf97a87593652137e37db277162b498489434

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