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Paper Citation Record · LEDGER

Phyllotaxis in a Keller-Segel model

As of 21 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2509.06498.

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

pith.paper-citation-record.v1
2509.06498 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T23:37:13.617319Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

26 of 26 outbound references displayed

  • verified exact0
  • verified fuzzy17
  • unresolved9
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8b39b8d3-e661-43ea-8a00-75687990f37f · outbound

This paper cites Levitov, Fibonacci numbers in botany and physics: Phyllotaxis, JETP letters54, 546 (1991).

Phyllotaxis in a Keller-Segel model Levitov, Fibonacci numbers in botany and physics: Phyllotaxis, JETP letters54, 546 (1991)

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.850295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:11.580232Z digest=sha256:65f9e07029dc39082cda68e439ffd43a063c0341acf363db3a63587f4e791d7a

Observation f4d8ae1c-4101-483f-bd6e-027b2afa0139 · outbound

This paper cites (b) A Fibonacci spiral (2, 3) pattern,S= 1, G= 1.2.

Phyllotaxis in a Keller-Segel model (b) A Fibonacci spiral (2, 3) pattern,S= 1, G= 1.2

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.857994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:11.543586Z digest=sha256:aba470ec865cc6e629ca738c0fbd99b3f4f358162cc441803192864a995908e2

Observation 42cadc21-88c2-449f-838b-f13dc87b1564 · outbound

This paper cites Adler, D.

Phyllotaxis in a Keller-Segel model Adler, D

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.842435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:11.664311Z digest=sha256:11283119dd24934125ff3328919b4f411cdab7006ead0122567d1942d8652ccd

Observation 7472d1a9-52af-4562-a72c-ae1138b79cd5 · outbound

This paper cites an unresolved cited work.

Phyllotaxis in a Keller-Segel model Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:37:14.835135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:11.787949Z digest=sha256:1fb572103f1f06e8a0c0809556bed681d14056e2f396bcd4e86deea683e35943

Observation f282f5fa-0e08-4bfe-b928-9db942e1144b · outbound

This paper cites Hofmeister,Allgemeine morphologie der gew¨ achse, Vol.

Phyllotaxis in a Keller-Segel model Hofmeister,Allgemeine morphologie der gew¨ achse, Vol

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.827348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:11.875718Z digest=sha256:08ba1545cc3b086c48edd3bb2959143c5934358876f830440857f34a8d25364e

Observation 595d466b-79cf-4946-aaec-c9bd15b880ef · outbound

This paper cites Airy, On leaf-arrangement, Proceedings of the Royal Society of London21, 176 (1873).

Phyllotaxis in a Keller-Segel model Airy, On leaf-arrangement, Proceedings of the Royal Society of London21, 176 (1873)

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.819309Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:11.958855Z digest=sha256:8294c0d3c26440a3eae54a6baf4e6536035fe50a1abc64726b54e7b2b2740aea

Observation e11b1034-f848-48c5-ae64-b1b8ff820f68 · outbound

This paper cites an unresolved cited work.

Phyllotaxis in a Keller-Segel model Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:37:14.811728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.044102Z digest=sha256:fc33b8bd08cecb7bbff2168515cd56d042f04a18a5c7cf24ef531b163e44461e

Observation 2ad9ea3a-91bd-4131-98d2-1c95aab9e591 · outbound

This paper cites Douady and Y.

Phyllotaxis in a Keller-Segel model Douady and Y

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.804254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.106730Z digest=sha256:6ede499e651bf12b4909c194bfa4516467f82835ace50a1cb54af8a8da520577

Observation 3879ed96-36a2-42c3-99f1-01be2c093f19 · outbound

This paper cites Levitov, Energetic approach to phyllotaxis, Euro- physics Letters14, 533 (1991).

Phyllotaxis in a Keller-Segel model Levitov, Energetic approach to phyllotaxis, Euro- physics Letters14, 533 (1991)

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.796854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.145427Z digest=sha256:f3e86cca9bfce54d8c6b6b54521603dbca5e0b4123c588ac325e2349bc58dc9d

Observation 0d01bce9-575c-4eb7-99e3-5989210e199e · outbound

This paper cites Nisoli, N.

Phyllotaxis in a Keller-Segel model Nisoli, N

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.789460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.205903Z digest=sha256:313a298bde637ee324ec963d8fe0d0ec623959da08f8618771794c77b3cefd80

Observation 638fa770-090a-4111-9d04-b7bcd6b22a1f · outbound

This paper cites Dumais and C.

Phyllotaxis in a Keller-Segel model Dumais and C

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.781882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.261450Z digest=sha256:5dccce8ae67e4422f0b3c965e49bb55a0bab5a59ff64ddca4e5080c97147ce55

Observation 5f0b3315-3fdb-4499-8bb3-2fdff9c3c30d · outbound

This paper cites Shipman and A.

Phyllotaxis in a Keller-Segel model Shipman and A

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.774485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.351676Z digest=sha256:050d1e8152f438b2f539b6d627b82f7e9eab0bec3af480d1054412af474829d8

Observation 0a856443-3cc1-41dc-9b59-55cd138ede17 · outbound

This paper cites Zhao, Auxin biosynthesis and its role in plant devel- opment, Annual review of plant biology61, 49 (2010).

Phyllotaxis in a Keller-Segel model Zhao, Auxin biosynthesis and its role in plant devel- opment, Annual review of plant biology61, 49 (2010)

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.767071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.400240Z digest=sha256:2fabf4c1a50c73b8b2e5ca3553b0a789a55381222d87935014310fcc705f89a3

Observation 4cd02489-6024-4db3-ba5b-d63d30c122c6 · outbound

This paper cites Vernoux, F.

Phyllotaxis in a Keller-Segel model Vernoux, F

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.759004Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.481580Z digest=sha256:5d4562dd70151153335942d3e43bf8ac4a173d11f8cdb57c3bbfa90c715adbc4

Observation 8e9626a9-6835-40b5-a268-45b0dd9a580c · outbound

This paper cites Pinon, K.

Phyllotaxis in a Keller-Segel model Pinon, K

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.751210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.514518Z digest=sha256:d71be5668e64b871b2898b6550210640d9473a0b5a3d7a25c6c966f585a9e395

Observation 40d8a78e-8f7c-46e5-8ad1-0a5adc28acd3 · outbound

This paper cites Reinhardt, E.-R.

Phyllotaxis in a Keller-Segel model Reinhardt, E.-R

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.743348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.615023Z digest=sha256:4a3408b94264b4ca26be2d311a0caf7b1423f8902213ddcb47a9f2d6169db61a

Observation 66996c19-e7af-4b95-93be-aa3f2ea73180 · outbound

This paper cites an unresolved cited work.

Phyllotaxis in a Keller-Segel model Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:37:14.735527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.693797Z digest=sha256:f109464ce39d79e2fa34670f675e082695a461ac6200d7e8725b8a6eab083336

Observation 54a7df97-9cd3-4b6f-b377-eeb9e6d4b1a1 · outbound

This paper cites an unresolved cited work.

Phyllotaxis in a Keller-Segel model Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:37:14.727736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.778501Z digest=sha256:1cd4d1bf67c1307b82e35847c6c56685e63286f63c7dafbd812ff1aa0ce57f70

Observation b5afeeee-c8bc-460f-a96a-49fe5b51378e · outbound

This paper cites J¨ onsson, M.

Phyllotaxis in a Keller-Segel model J¨ onsson, M

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.719883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.844520Z digest=sha256:68937a88fc6f88cdfbe62f7e9d0e45da5f0a8ea469552c24aec9b22e75e7f103

Observation 3d727b4d-fefd-44c1-8c65-0d1e4ed8d9b0 · outbound

This paper cites an unresolved cited work.

Phyllotaxis in a Keller-Segel model Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:37:14.712149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.894573Z digest=sha256:eaab23425d4ae037410f87a7af293a3db1d46506ec4efd9d9ea19909e2ad5c6a

Observation 212e54c2-ba1b-4f0d-99a6-d0df2f9defbe · outbound

This paper cites Pennybacker and A.

Phyllotaxis in a Keller-Segel model Pennybacker and A

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.703621Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.960085Z digest=sha256:a5131de0577f15c8ee502cc6c1a8fcfb90b21ee9137308fd20211e5876d50b92

Observation 5a4b008a-eeb7-4095-ae57-89e2a32c9574 · outbound

This paper cites an unresolved cited work.

Phyllotaxis in a Keller-Segel model Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:37:14.630412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:12.973162Z digest=sha256:02ae582ca7e20ef269aafac51ed276b2318c4e99aebbfd32ab0043c58a6a036a

Observation 30e8eed1-50bc-4783-8772-bcee871af7dc · outbound

This paper cites an unresolved cited work.

Phyllotaxis in a Keller-Segel model Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:37:14.488496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:13.059003Z digest=sha256:a1e14bc49c266ca7ffa00eb79b3162bf3acfaed881a2fde09e7efe9f68848544

Observation da044508-b417-48f6-866e-48e6d5ae138a · outbound

This paper cites an unresolved cited work.

Phyllotaxis in a Keller-Segel model Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:37:14.379397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:13.276377Z digest=sha256:88c8e82610874f6cf8446d26bcf2fd54219944443e43742ee152b9e6b612b0b5

Observation b42e3181-b817-4443-88cc-ce8d788065de · outbound

This paper cites Arumugam and J.

Phyllotaxis in a Keller-Segel model Arumugam and J

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T23:37:14.052469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:13.444994Z digest=sha256:406f0f0ba2c51ff7198099415a82e94db5f49eeb6b3432fb880995a2258a3261

Observation 9585a2be-3023-4231-ab54-e600f5d0fba8 · outbound

This paper cites an unresolved cited work.

Phyllotaxis in a Keller-Segel model Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-04T23:37:13.833510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-04T23:37:13.617319Z digest=sha256:ca590b0b4f1b44c5ee66e9914388c9b46660acaf80ee3ed9f5f439f0ebc83fd0

Pith citing papers

No inbound Pith citation observations are available.