Pith. sign in

Paper Citation Record · LEDGER

Pattern formation within phenotype-structured chemotactic populations

As of 9 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 2026-08-08T06:32:00.761636+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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.186903Z digest=sha256:a71cc4630eafccb18756275989cf33f2dba59f1e5cd8d8ad61de0841a427272a

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.271552Z digest=sha256:05b9d7553d73b4fad775b84f166e67e506dc76bdf8a48d24108a0a5767c999b2

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.332085Z digest=sha256:1421fc84e4c66311e388f4252ad46baf4fada4ba90e61c4004f910e7f8d3cb2a

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.390880Z digest=sha256:dd1f621e0076741c729b71c5594a879fcb2eac5afd93d5ff00c7eff63dfde41c

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.450267Z digest=sha256:082c8ee2a17e076dc215407186e70b9b4333661a5741197370741a36022e3fa2

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.499474Z digest=sha256:398bc5655564ac32ec262bc09e2cdf477ee0585d03ca051f2e05228c297aa7b7

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.552277Z digest=sha256:5f8f5c758606d3a586fa4a6ffde5a3aa3093727abb31b622367a821b6741a784

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.607714Z digest=sha256:c33940e1a350f1834508966fd9ff477350d6325e0b0a006ee135054cfddabac8

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.644876Z digest=sha256:3c9bbdffcddc76bb8fdca9644db60168be2451b048739155637f2cfb361d5baa

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.700789Z digest=sha256:c9c7d8e0300cc0a5d62057b3caec0b4a4e5e81147cb6352a3f87f00a0e03b4fc

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.744729Z digest=sha256:7403c9944a1ffd03e18d1095e0b23ecf7659c957cb6c7999e4e9552cb40f2ea6

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.816530Z digest=sha256:bd754c4f3e0258b66d2b64bf274f490b905d4a6a1b427582e9214ffdcef47cde

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.857717Z digest=sha256:506af9bec64775f898dc4a31f4e8adb2c8f113d62f586a085fe7e2a84da31144

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.893093Z digest=sha256:44bbfad2dc405fc737c1562dc8cdd387666bc132c890c117d7f43a964b570943

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.941715Z digest=sha256:866c9e4228cac8239d62f6cfdaf0526f419ac4babd93bbbc9f5f22525dc3937b

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:32.999970Z digest=sha256:da5ef99f2bfb4f1c6e50ee077109a6c5e062ba52035412f72e1cb41763c120c9

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.050431Z digest=sha256:356316be426ec9aa13622b5057845f1f16d2a5d9ddf247e4987752ebc085c87e

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.108368Z digest=sha256:32447465bf9c938fc88d91a4917b2566c4b1fadfc9081cc8a1b50dc2744b6951

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.173352Z digest=sha256:1f65289ce985ac343bbb075d08b6136a75c980c8fff036d4fdb156457ab6877f

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.221003Z digest=sha256:8aa16bb9f916322fc597b0eea4652c5ed5b11a0e7630d2e8a1a920a6c26864d4

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.269213Z digest=sha256:4eb50714c3c37431e99816e5132939d4e9bb119faa846073ca8170f946e754fa

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.338580Z digest=sha256:85304c1934082164bcfc5d6ec66f59e13714bf51eb72391d7baa05967a0fabea

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.376382Z digest=sha256:64fa13240a785409d3bcae274a4d68d45f54a75b5c15e6efb1eb022a1c5c87e4

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.433941Z digest=sha256:e95786c1aefef13a70761c62324bbd717930eb3db94c23e736a5acf2cb085abb

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.496375Z digest=sha256:113747ee9cf4fa3c744e8f8a41aa7996571dbffb4b47bbca77f65f8bdca7b869

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.538555Z digest=sha256:e22c8aa79363759af272321cb5772f0f7658416182d7296d041681030e1ef7db

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.599367Z digest=sha256:ebe6f44bb4ea79ec67329f1a4b9346a91a48e50d5a5579f46c7252e574c88c1b

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.663591Z digest=sha256:b0a58b5c900889058ee169df67c65215b44d087e0496fa92692b85919c2066e5

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.717450Z digest=sha256:4c7ea08eef9c4327788a3aa6488a9d609a5f3473399ef93a873adbe461e9c7fd

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.722693Z digest=sha256:e0cdfea9f4b0f8b0f9841fc7f40ef1d69f12c4bbdfd93e57b7f6346eb19c3c89

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.776251Z digest=sha256:680095c53ddb13541875840e7e2b9e043ed517ad3094fb5b4083e96a1dd34616

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.845068Z digest=sha256:f25c39d67d24d0e7e6be0065a079cdb0d47a26e8c7e4133d42024e49529343d4

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.887185Z digest=sha256:d299aba61edfce2b911e25a1ba48fe7da1628d5a17a6a80bea8371960c25ab1f

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.923196Z digest=sha256:6b32b96cdae54b8cac4e78defa2bb59cd69695f48d8f36b72a604687ad24a194

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:33.990614Z digest=sha256:8567cdde4d313fc496cc15636bfac83902ea6a3ffaa94e8e1f6932f511f95c4a

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 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T11:14:34.061052Z digest=sha256:4ec5d19797b5765ceb9b55275929c12736d9a83ca240b108f51c1dd25d73e648

Pith citing papers

No inbound Pith citation observations are available.