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Paper Citation Record · LEDGER

Partial Deranged Bell Numbers and Their Combinatorial Properties

As of 22 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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.168473Z digest=sha256:96fdd5ec5ac6f8e6b18addbe4e9d634e1aa98a1cfe7f30640ff09e337bb4ad28

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.238371Z digest=sha256:f3e3c0ca7a1cad97240e974ffc1f773f227f56197a13c1ef972ee4a4bb429329

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.298244Z digest=sha256:d7831936415e7f2466b16eeb8a68a14f79933902274bcde54a7dbee4672d8b7a

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.394579Z digest=sha256:b25222ed90608109855bdf4603b3a9bf9bffd53eba98f02c6c5356c581ea81ab

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.499329Z digest=sha256:275dcf0ee64647d1613b9cb2543526264b31d6b046dd9d0e68bc586a74dc413f

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.566423Z digest=sha256:04a736bcf181a0055ed6e17959392c6d619fdb20e05e05402859c4a61769a0a9

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.632150Z digest=sha256:63f9b503c437fa91438616a5d50091bfff686e4806f1eb6c10722204af934b1d

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.688122Z digest=sha256:bd032fdd49f30ca9877efce2a300b18e50216e2ca40a17e84a3d4cc084d933ed

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.747338Z digest=sha256:aba837e75c920d7fa2d33eec55280ec3adb6ed12c421c2e1fc02f6769a79edbf

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.818127Z digest=sha256:452ebec024ee1dfef6ee4cc5e032812b2e001c6c668230dfa3b9556bb53c1a97

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.891024Z digest=sha256:a8c9f936b6e11b29a0bb00349b97928ddfc35f1b28aa229e39561ed869e9791a

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:00.976215Z digest=sha256:952baef7d5b470db4ecc39b0454f67c3135e396479a1aceba107622f89c0d17d

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:01.053006Z digest=sha256:cb4071c87dcd17b93a3ba521d6ee4125dc4c1a5831ab422a2b31316995e93e4a

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:01.117729Z digest=sha256:52c64db5d2c826dc7fc287a99e0c354786b74d36a11ae919e300254e09c3bdd1

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:01.216187Z digest=sha256:5a0a621c01470dd5d0d3f03b4bdfb25dc5661d8d457a3db2ae75247c27859b00

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:01.282206Z digest=sha256:a3318acd04de8170a295fc2f1c34f0ef08d9c195f3a056624c0a39a4525724fe

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:01.320941Z digest=sha256:1f532f5855a2a653bcb7dc749155a949b9befc5ea5f02b2229ff0d148ab0f444

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:01.334044Z digest=sha256:4b0ae25f8a33c3d13c80ce42450e51b0479bfaf2961724b32d1401cd8542debc

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:01.419554Z digest=sha256:5cac1e4a2fd35c254d861fe707fb5ccc7b8142882defb4e7655e6f7461f01029

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:01.572040Z digest=sha256:ce321276bb734590ab20ca2a863a0cbce6568085828f8f22b7a3c0049e7f8b9b

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:01.738503Z digest=sha256:8e8c2923e3cdbe0357d6d7c7c188cd5ba91b16bd687470e4a18126a92b916b11

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:01.864049Z digest=sha256:d39174455706c3194b223086f97bbff8e7aaa079ed1f3098aad8ea361b1a540b

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:02.011077Z digest=sha256:81975c0d6babb83ab4372f30bc1e1cb0ddade7afa6f8e0f18946427c9aa96770

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:02.134513Z digest=sha256:c6f9b080024088c2dd18c9af5bced772f113db23d2e7aa0c993367950462b67b

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:02.281140Z digest=sha256:90afd6f1a9a3af7cb0c4ab84fbbf75d6cc73bacc3bb2676249f9e57308ca4d26

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:02.434425Z digest=sha256:d395e5401125f7b970c48a7ee83de26b3ad4c8d47236e5526d93c4eda3d47fe5

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:02.440624Z digest=sha256:25d90fa95c885a915c83f8cff47696adc8bd128e34e71fa8046b8c332fe75aa1

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:02.448204Z digest=sha256:ca7b2392fb5b5624e0b101ac98eb870d673c073e429ac067f0bfc01e5d782753

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:02.455289Z digest=sha256:bae5d9eabdc404d111714f9d958c937102f9888f69465b0a929a638321d83c6f

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:02.460703Z digest=sha256:eb841458ba9d81e9a01252c78499c4ebaed3c070e134a9836b42da47d162546b

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-06T12:45:02.467480Z digest=sha256:8a80c508e4e6a6e4b7c2c7e1ebcbfb7d6079a139c26490e07a58392f4e523a58

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-05-12T00:50:29.420224Z digest=sha256:d343b7f848317e096a773c19fd1ad1408cfab527be7c11f3c9a5e82954f1bed5

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=sha256:00ca250273ebba664bc242a294906757566df521d93d98921b002930a00e118d

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-07-03T21:51:48.776220Z digest=sha256:8127f6209a4f25cca9180f67efe32cf56c4e11eabfb484d168d2f6e89ab46f84

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:cff967b4efa7329643f1bb646ea39bcaa4d699b199ccc915fd45b10fb7a144c7