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Paper Citation Record · LEDGER

Pattern formation within phenotype-structured chemotactic populations

As of 8 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2506.03389.

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

pith.paper-citation-record.v1
2506.03389 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:14:34.061052Z

measured 36 of 36 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

36 of 36 outbound references displayed

  • verified exact1
  • verified fuzzy14
  • unresolved21
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 934da8a8-3e6e-41dc-acaa-9e430704ea4d · outbound

This paper cites Ackermann, A functional perspective on phenotypic heterogeneity in microorganisms, Nature Reviews Microbiology, 13 (2015), pp.

Pattern formation within phenotype-structured chemotactic populations Ackermann, A functional perspective on phenotypic heterogeneity in microorganisms, Nature Reviews Microbiology, 13 (2015), pp

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:39.199680Z

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=2026-08-07T11:14:32.186903Z digest=sha256:384fb1b7cffa7f6072a547143dcb007e740d9e558fcfde349147cbb73963d314

Observation 7c5cc0fb-d6a9-4c65-85cf-f81eb1d9fbd2 · outbound

This paper cites Almeida, J.

Pattern formation within phenotype-structured chemotactic populations Almeida, J

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:39.030787Z

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=2026-08-07T11:14:32.271552Z digest=sha256:0a5b4378d3de76c73258ae8a3eec4e56afc772dd15883b4868ba59d0c272957c

Observation 6d346481-164e-470e-a020-a58423159be2 · outbound

This paper cites Bellomo, A.

Pattern formation within phenotype-structured chemotactic populations Bellomo, A

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:38.852959Z

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=2026-08-07T11:14:32.332085Z digest=sha256:e418cb42952b7b92494bf0a86a4759ab43ba3e8ff7f6076036ebe1eeaf454cc9

Observation e29cb644-b999-4803-808d-eca1023f0bb9 · outbound

This paper cites Carter and K.

Pattern formation within phenotype-structured chemotactic populations Carter and K

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:38.654896Z

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=2026-08-07T11:14:32.390880Z digest=sha256:74bb05fed27f55c30d5c1e39b5d3121ec6ac59b91fba11a586de3152d7a25d40

Observation c970d2f9-272e-4403-8c3d-eb0f52c7596d · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:38.411856Z

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=2026-08-07T11:14:32.450267Z digest=sha256:a2f6d2042798c8ad924820c21f9953f615e28ceb33852bbac4bc80117c52ce82

Observation 5321dafe-3aa9-4407-8ec6-4cc7ec0d7c65 · outbound

This paper cites G´enieys, V.

Pattern formation within phenotype-structured chemotactic populations G´enieys, V

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:38.288852Z

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=2026-08-07T11:14:32.499474Z digest=sha256:c46c9f160af420035c8875156289369e7692eec5589c71615458f91412dbc58f

Observation c95cefec-c7df-4949-a809-612bb9ae45ce · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:38.190380Z

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=2026-08-07T11:14:32.552277Z digest=sha256:a5969cc9aeac1aaf77ca59e2880bade480f3fd956a50b32c02ada06a0e932fa5

Observation a6418825-583e-47a7-b6e5-eb89ec8ae035 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:38.071508Z

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=2026-08-07T11:14:32.607714Z digest=sha256:bd004cbaaaf01f11d6cfcb85bee7eb0fbba34554c1e94831e039b0aeec246ea0

Observation f462c96d-369c-4599-96dc-0d241a20fe9a · outbound

This paper cites Keller and K.

Pattern formation within phenotype-structured chemotactic populations Keller and K

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:37.967545Z

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=2026-08-07T11:14:32.644876Z digest=sha256:c7c2b9931cef1bb3f2ede154233c12004aee0ce9b5421f4afb90596132b35fce

Observation c472a1fb-b8e8-4335-84ad-3051f83a7daa · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:37.869610Z

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=2026-08-07T11:14:32.700789Z digest=sha256:f89f4d8dbd74f2440d924b6de2329703faccc9d2241f94f02d560605899a27ab

Observation 932b7ce8-aa94-48e0-b021-fa2e94bc7426 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:37.775159Z

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=2026-08-07T11:14:32.744729Z digest=sha256:becb95e4d993ac27f15d0f383f6c50a28c644b0ea6afbad6dec2955860defb99

Observation 413d4202-10ec-4f64-aeeb-d2e557653a05 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:37.663833Z

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=2026-08-07T11:14:32.816530Z digest=sha256:061e3d29f49dda3230245efb47ce9ec7bc21554af700f01557f72eb7585136ec

Observation 60e9cd59-aafc-4b77-a3a2-cdfe2464243c · outbound

This paper cites Lorenzi, F.

Pattern formation within phenotype-structured chemotactic populations Lorenzi, F

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:37.600942Z

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=2026-08-07T11:14:32.857717Z digest=sha256:2fef9348f1d08d726cbfb0c31a9aaa38f98a507ead8ed166ea3e8657b7b8be60

Observation 53fb7a8b-1376-4525-8e5b-015eb92c4176 · outbound

This paper cites Lorenzi and K.

Pattern formation within phenotype-structured chemotactic populations Lorenzi and K

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:37.514264Z

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=2026-08-07T11:14:32.893093Z digest=sha256:6100fa7cb0ce8136fb065beb687881fb6630fd5e45f0cd1a0924a6b0b84cbbc1

Observation 539abe3d-b455-4610-aee4-cf4e1e4e8f44 · outbound

This paper cites Lorenzi, K.

Pattern formation within phenotype-structured chemotactic populations Lorenzi, K

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:37.402719Z

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=2026-08-07T11:14:32.941715Z digest=sha256:90a93b041e570c44585b5ac99cc6a82d4c34d0af2f017f06d836dd4b16bc8c26

Observation e411bc07-63ec-4f11-a29e-ddad0e029475 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:37.279995Z

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=2026-08-07T11:14:32.999970Z digest=sha256:9bdc3838eec240b03a507847e5c6943fa3f3e46d1f5e66baab633c3176a51014

Observation f1b5b916-fbb0-4123-bdd7-6208fb937ad7 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:37.204485Z

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=2026-08-07T11:14:33.050431Z digest=sha256:ab09233f93b4298f356ec118006041014a378b4318a1e52cc32a5b51e3044963

Observation 63d556bc-d675-48d8-a34c-2aedde34a3c7 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:37.076046Z

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=2026-08-07T11:14:33.108368Z digest=sha256:582570293f1c7d20591097ed52021ab7a92ccf6d94efcf877a290bb2a17b2622

Observation 361a7907-3926-4052-b889-0a7965fb178e · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:36.945315Z

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=2026-08-07T11:14:33.173352Z digest=sha256:bb17a6812f8afabb28881d1162a27788ed2db6bef3eea5a9f80af65d49119581

Observation c3a8e9b3-5805-456b-9990-bde1d8926a02 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:36.812748Z

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=2026-08-07T11:14:33.221003Z digest=sha256:a18cb7ba376b407fe0efca477c227d1711d9c2bf847b98c5db9c377bbba97249

Observation 86a9f75b-3934-46e7-9d80-94e90c193942 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:36.681342Z

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=2026-08-07T11:14:33.269213Z digest=sha256:e8658ba9fb417848b16025659eac1a4a97d70aa22b107e9f62953b54738dbf40

Observation 9550994b-0942-4459-b496-7a68b69a8561 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:36.574501Z

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=2026-08-07T11:14:33.338580Z digest=sha256:931661c42fbb635fc9238dafbba268b04a02992bad309be142becc3793f94f0a

Observation 9ab6032c-0e28-4479-9820-06deae9d22ac · outbound

This paper cites Perthame and S.

Pattern formation within phenotype-structured chemotactic populations Perthame and S

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:36.455147Z

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=2026-08-07T11:14:33.376382Z digest=sha256:1e64d2c5b5a760b9366df79d512603127e45bb64625f5b6c0af668dcfe9a4f20

Observation e7637a6a-639e-4bcf-8135-b2a1d99b5998 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:36.343341Z

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=2026-08-07T11:14:33.433941Z digest=sha256:067888843a7dc31e95aa3200f85648f676d01b424808d41befe4c5c4b5e22a9e

Observation b353af88-32e5-4a31-a33b-b980714fad2a · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:36.216190Z

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=2026-08-07T11:14:33.496375Z digest=sha256:f815c3792bb7fbf32ff83e05b2d1d33630858630b14f1fa04477af08f50d9e31

Observation be9ef835-7161-4942-9f68-0d4692530b14 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:36.098339Z

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=2026-08-07T11:14:33.538555Z digest=sha256:abcc951db399f8471266b7534e25578a9b8684fc97b0d37f8573946852c1997a

Observation 23d2cb6a-6e12-4d2d-805f-e3f9c4501fb6 · outbound

This paper cites Rietkerk, R.

Pattern formation within phenotype-structured chemotactic populations Rietkerk, R

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:35.952931Z

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=2026-08-07T11:14:33.599367Z digest=sha256:9170e6e284a3e34258608a7d7dd850cfe96f59e0d8a7cec995b71d6bfb020f0f

Observation abd4f0d7-845e-4c89-ad86-3bc7ebb549a1 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:35.788227Z

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=2026-08-07T11:14:33.663591Z digest=sha256:69ae11e076897ccb6064f8737dcff2c1a1989b1616085f1956b3218e2d8488b8

Observation f1f35433-01ec-4f82-bacf-3ad8421f6c84 · outbound

This paper cites Schreiber and M.

Pattern formation within phenotype-structured chemotactic populations Schreiber and M

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:35.629270Z

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=2026-08-07T11:14:33.717450Z digest=sha256:2d30520658af585739006320f67854fb49bcf580c18c322f06865a320568d274

Observation 77223e0d-f6cb-454f-84e2-87e7672b9b42 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:35.512532Z

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=2026-08-07T11:14:33.722693Z digest=sha256:3c8e3ae6c9e3a5fb8985bf586d081f721043f718e6d988ccee4d3c349c0fbef5

Observation eb99ce98-9598-4795-b73a-29d209feb3a3 · outbound

This paper cites Tao and H.

Pattern formation within phenotype-structured chemotactic populations Tao and H

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:35.357134Z

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=2026-08-07T11:14:33.776251Z digest=sha256:d3996957ee6a7d3080f907b1951d9dad2c239dd1615b9f077cb1b3968193f15f

Observation 77b3f3bb-7149-40ff-99ad-c1b88520cb88 · outbound

This paper cites Thiessen, M.

Pattern formation within phenotype-structured chemotactic populations Thiessen, M

Reference 32

Resolution
verified exact
raw_fallback, observed 2026-08-07T11:14:34.363579Z

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=2026-08-07T11:14:33.845068Z digest=sha256:be4b071d70528d65868b4f53be67c1ef79ce994ca00cbc7999176b7b6f118edc

Observation adbb9fd2-66c8-4b68-b8c6-32f4e0871f01 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:35.206935Z

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=2026-08-07T11:14:33.887185Z digest=sha256:2b44f4cc0a0d7cbd77a6bcb24ef24b9f7d2236b35590fd2b93aa3a349465f093

Observation 0b8d5d33-00ef-4232-aab6-14041a9929de · outbound

This paper cites Verhulst, Notice sur la loi que la population suit dans son accroissement , Correspondence Math- ematique et Physique, 10 (1838), pp.

Pattern formation within phenotype-structured chemotactic populations Verhulst, Notice sur la loi que la population suit dans son accroissement , Correspondence Math- ematique et Physique, 10 (1838), pp

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:14:35.052730Z

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=2026-08-07T11:14:33.923196Z digest=sha256:b9ee0b3d50372904f983078675bc35de0e6c43b72ccf4524e577561b4de9326a

Observation 870b60a4-894f-45ce-ba1e-19329ac3e599 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:34.788480Z

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=2026-08-07T11:14:33.990614Z digest=sha256:943fb8835fe39aecb46289a7c9a60e49b4669d9a9eff58c1ccfa1aea6172c5a1

Observation d16bee30-8e70-43cd-95d9-66cdcf469188 · outbound

This paper cites an unresolved cited work.

Pattern formation within phenotype-structured chemotactic populations Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:14:34.617366Z

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=2026-08-07T11:14:34.061052Z digest=sha256:2c7c93bbcc3d2d2871aacbb41548c3f8cf1cb5c8f311de90e2ab223c07584905

Pith citing papers

No inbound Pith citation observations are available.