Paper Citation Record · LEDGER

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions

As of 8 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:2505.23988.

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

pith.paper-citation-record.v1
2505.23988 v1

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:43:29.945546Z

measured 45 of 45 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

45 of 45 outbound references displayed

verified exact21
verified fuzzy5
unresolved17
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c4b9af7e-cdce-4d7c-ba9d-2814f41e5315 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:43:35.811298Z

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.

Observation 8cd42cdb-df20-4dec-b9f8-d168549bf11c · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:43:35.648677Z

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.

Observation 57f9b39d-3210-4440-95d6-674522936871 · outbound

This paper cites The paper is organized as follows : In Model and Methods section we d escribe in details the methods required for all the 3 objectives as described above.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions The paper is organized as follows : In Model and Methods section we d escribe in details the methods required for all the 3 objectives as described above

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:35.502672Z

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.

Observation 62482942-43a3-4337-8414-acb19d2009f9 · outbound

This paper cites W., Ottino-L¨ oﬄer, B., & Kardar, M.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions W., Ottino-L¨ oﬄer, B., & Kardar, M

Reference 4

Resolution: verified exact; doi, observed 2026-08-07T12:43:32.683216Z

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.

Observation 8655ff63-9123-44ca-84ea-c43973775bd2 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:43:35.229099Z

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.

Observation 87e24cb8-80f6-4701-8f02-8545c18fd305 · outbound

This paper cites RESULTS Table II: Summary table of solutions(Richards Model).

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions RESULTS Table II: Summary table of solutions(Richards Model)

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:35.069462Z

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.

Observation 36e21bb0-aedb-4638-a65f-6826e6cb1b34 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:43:34.816022Z

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.

Observation 3265f1e6-ff90-479f-85f4-57237b3d57a5 · outbound

This paper cites Estimation using residual error and log-likelihood surfac es First we take up ( 14), where we assume a Gaussian distribution of the residual Errors.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Estimation using residual error and log-likelihood surfac es First we take up ( 14), where we assume a Gaussian distribution of the residual Errors

Reference 8

Resolution: malformed identifier; no resolver link, observed 2026-08-07T12:43:26.409898Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a21231a-3617-4582-a02a-3125d9afa173 · outbound

This paper cites Mathema tical Modeling of Cell Growth via Inverse Problem and Computational Approach.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Mathema tical Modeling of Cell Growth via Inverse Problem and Computational Approach

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:34.551579Z

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.

Observation 1affa38c-717b-41c9-8aa6-ec002fd1df27 · outbound

This paper cites (1937) A study of the diﬀusion equation with increase in the amount of substance,” and its application to a biologi cal problem.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions (1937) A study of the diﬀusion equation with increase in the amount of substance,” and its application to a biologi cal problem

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:34.251485Z

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.

Observation b5499fb1-c7c7-40b5-b907-2c58c0a50668 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:43:35.367030Z

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.

Observation 2315b1e6-0db7-459b-b003-839dd4f4fd76 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:43:34.002430Z

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.

Observation b31ee867-50aa-4c05-a680-968acad2a3d3 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T12:43:26.972422Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7d4f7999-8da0-4699-9bd8-501045886030 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 14

Resolution: verified exact; doi, observed 2026-08-07T12:43:32.428755Z

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.

Observation 8eb27e42-ff51-4e9f-a3c6-6842ad801796 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T12:43:27.125312Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c7689fc-ed55-48c2-bf30-9cebeec418e1 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 16

Resolution: verified exact; doi, observed 2026-08-07T12:43:32.286340Z

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.

Observation 9936def8-a2c6-4012-a0c8-919033274d68 · outbound

This paper cites W., Jin, W., Moroney, T.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions W., Jin, W., Moroney, T

Reference 17

Resolution: verified exact; doi, observed 2026-08-07T12:43:32.162545Z

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.

Observation 3388c505-e74a-4e28-a22f-d62384893f84 · outbound

This paper cites Q., Landman, K.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Q., Landman, K

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T12:43:27.415764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b31fa920-2f4e-4542-a412-724710437241 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 19

Resolution: verified exact; doi, observed 2026-08-07T12:43:32.003001Z

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.

Observation 4d4d87f7-cf0a-41b9-9528-6a608f2d9e58 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 20

Resolution: verified exact; doi, observed 2026-08-07T12:43:31.880133Z

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.

Observation f89c5ae5-13e3-40e6-885a-4396ce82aeb1 · outbound

This paper cites L., Rutter, E.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions L., Rutter, E

Reference 21

Resolution: verified exact; doi, observed 2026-08-07T12:43:31.775519Z

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.

Observation 165959b0-a066-44a6-b678-7038e4bcc69c · outbound

This paper cites J., Baker, R.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions J., Baker, R

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T12:43:27.846418Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 40ebc3be-193f-4e5d-9d91-1fd4604be207 · outbound

This paper cites M., & Baker, R.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions M., & Baker, R

Reference 23

Resolution: metadata mismatch; raw_fallback, observed 2026-08-07T12:43:33.096102Z

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.

Observation e008c3d3-1cbb-4c97-accb-4c13d0fea024 · outbound

This paper cites J., Carrillo, J.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions J., Carrillo, J

Reference 24

Resolution: verified exact; doi, observed 2026-08-07T12:43:31.654636Z

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.

Observation 795dd0be-da19-4246-a456-24d5732d5e9e · outbound

This paper cites Communications on Pure and Applied Mathematics 3(3):201-230 https://doi.org/10.1002/cpa.3160030302.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Communications on Pure and Applied Mathematics 3(3):201-230 https://doi.org/10.1002/cpa.3160030302

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T12:43:28.146351Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b3565726-4988-4f60-a155-f5c1e1dd55f4 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:43:33.828789Z

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.

Observation 31d38c71-4f0c-458a-8e25-8e6f2c87ce0b · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 27

Resolution: verified exact; doi, observed 2026-08-07T12:43:31.517701Z

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.

Observation d42ca09c-a670-4df4-ba04-b1ecab8dd258 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 28

Resolution: verified exact; doi, observed 2026-08-07T12:43:31.376819Z

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.

Observation 3ffe5098-6a56-4d23-9a6d-d8e7082e3d91 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 29

Resolution: verified exact; doi, observed 2026-08-07T12:43:31.266533Z

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.

Observation 69e3117a-e92a-467b-9ff8-fa342125ef48 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:43:33.659030Z

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.

Observation 91a42ffa-8396-48ec-b03a-be0f1782e104 · outbound

This paper cites W., Newell, G.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions W., Newell, G

Reference 31

Resolution: verified exact; doi, observed 2026-08-07T12:43:31.153339Z

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.

Observation 6f34ccda-9003-4291-8db4-db44be084b51 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 32

Resolution: verified exact; doi, observed 2026-08-07T12:43:31.048037Z

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.

Observation 2fbd7523-b476-433e-b8a2-5a90b37d059b · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 33

Resolution: verified exact; doi, observed 2026-08-07T12:43:30.913335Z

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.

Observation 739887fc-94ed-492b-a0a0-8d46e5714fc9 · outbound

This paper cites J., Zeppetella, A.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions J., Zeppetella, A

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-07T12:43:28.932141Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08d2536d-fc5a-48e2-8a94-f9161e397fba · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 35

Resolution: verified exact; doi, observed 2026-08-07T12:43:30.767620Z

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.

Observation 98a16450-fcfd-4be3-80de-66395f79a321 · outbound

This paper cites A., Mansﬁeld, E.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions A., Mansﬁeld, E

Reference 36

Resolution: verified exact; doi, observed 2026-08-07T12:43:30.691659Z

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.

Observation ca4e0f99-034b-42f5-8274-c41b262a2d3f · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 37

Resolution: verified exact; doi, observed 2026-08-07T12:43:30.554388Z

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.

Observation 6e39e358-b8cb-4961-be52-b87ecf69b3a8 · outbound

This paper cites T., McCue, S.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions T., McCue, S

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-07T12:43:29.318559Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e43b1ea-80ec-420f-8e45-5213203b1601 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 39

Resolution: verified exact; doi, observed 2026-08-07T12:43:30.428484Z

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.

Observation f6ccdab5-e46c-41e9-8328-6a9ebd442f5f · outbound

This paper cites K., Cohen, D.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions K., Cohen, D

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-07T12:43:29.549642Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4bfef8a0-3198-4560-b6e2-a772ce88da94 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 41

Resolution: verified exact; doi, observed 2026-08-07T12:43:30.278111Z

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.

Observation 238a3551-1128-4d4a-bdac-220f82592564 · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-07T12:43:29.701511Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ec48a3e-0ebe-43f2-84ef-a5d0e8f7f240 · outbound

This paper cites (1943) Introduction to the Mathema tical Theory of the Conduction of Heat in 18 Solid Bodies.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions (1943) Introduction to the Mathema tical Theory of the Conduction of Heat in 18 Solid Bodies

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:33.298506Z

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.

Observation 1a73cbef-4cdd-4519-89cc-55349431da0d · outbound

This paper cites an unresolved cited work.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions Unresolved cited work

Reference 44

Resolution: verified exact; doi, observed 2026-08-07T12:43:30.175985Z

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.

Observation 47cb4b96-d587-4328-9aa8-f31944bcad3f · outbound

This paper cites A., & Viens, F.

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions A., & Viens, F

Reference 45

Resolution: verified exact; doi, observed 2026-08-07T12:43:30.089084Z

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.

Pith citing papers

No inbound Pith citation observations are available.