Paper Citation Record · LEDGER

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise

As of 14 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2507.15103.

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

pith.paper-citation-record.v1
2507.15103 v2

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:52:33.783727Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T04:18:41.156926Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-11T04:18:41.313472Z

Reference resolution

28 of 28 outbound references displayed

verified exact0
verified fuzzy16
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 46c84b49-87d5-4991-a850-8b9e4de3dbf4 · outbound

This paper cites Amrouche and N.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Amrouche and N

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:37.500430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 003c2e5a-7f9e-47cb-9d47-3c6a80ed083e · outbound

This paper cites an unresolved cited work.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:52:37.477992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 72b6f70d-3f02-4deb-bdef-b305a0799d2a · outbound

This paper cites Carelli and A.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Carelli and A

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:37.458849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 897c4027-7fb7-41e2-a585-cf076c56a13b · outbound

This paper cites Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T15:52:31.741590Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01126494-71a3-4da3-83e0-c2769994180a · outbound

This paper cites Duarte-Rodr ´ ıguez, M.´A.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Duarte-Rodr ´ ıguez, M.´A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:37.433569Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e283ba50-2b1f-4a17-9394-b9f5a378faea · outbound

This paper cites an unresolved cited work.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:52:37.413835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2cdba094-23c7-41ad-bb4d-0ad39170672e · outbound

This paper cites Feng and L.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Feng and L

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:37.394068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8edde8af-8e25-4d31-a52c-702cd3bfff43 · outbound

This paper cites an unresolved cited work.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:52:37.374663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d8fa8f97-5c02-4496-a853-96fb67a0cc3d · outbound

This paper cites Friedl and D.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Friedl and D

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:37.357412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9d09ead1-cc3d-4924-9b9c-7250af118bfd · outbound

This paper cites Gilbarg, N.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Gilbarg, N

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:37.338726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1ded4edd-e060-47cd-8662-115ce97f0a8a · outbound

This paper cites Hausenblas, D.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Hausenblas, D

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:37.320953Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1812e882-dfd8-4a78-b251-d6b549788e52 · outbound

This paper cites Horstmann.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Horstmann

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:37.304222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation fba25f5c-a4cf-41c2-9ecd-1fbd0830ddaf · outbound

This paper cites Hu and X.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Hu and X

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:37.243820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1ede7a82-6eb1-40df-ac46-e771d6ad7f29 · outbound

This paper cites Huang and J.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Huang and J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:37.011796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c7133062-ae7b-4229-8968-9b03d619b514 · outbound

This paper cites an unresolved cited work.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:52:36.669973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 97a751f4-a5e9-40ab-ad11-a85fe741663d · outbound

This paper cites Mayorcas and M.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Mayorcas and M

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:36.409509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 242bc4eb-5364-4907-80b1-4873d01c8d95 · outbound

This paper cites Misiats, O.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Misiats, O

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:36.172937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d3ce0505-add8-4cc7-90d2-a5fee978eb61 · outbound

This paper cites an unresolved cited work.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:52:35.895777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b7d62259-e9d2-40fd-b197-16beb26ceb78 · outbound

This paper cites an unresolved cited work.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:52:35.585808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 15782063-29b7-4556-9c38-bf8a35a2bad9 · outbound

This paper cites Perthame.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Perthame

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:35.498345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 95a40ed1-238e-4063-8c5c-fc19fc9f333c · outbound

This paper cites an unresolved cited work.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:52:35.276791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation fa3bd962-5047-4442-8e10-2e904a1b9af1 · outbound

This paper cites an unresolved cited work.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:52:35.112558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 924fbc57-8d33-44d0-9442-92a954903bc6 · outbound

This paper cites Shi and C.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Shi and C

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:34.949543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9b605968-527a-4828-828b-32368f7790f4 · outbound

This paper cites an unresolved cited work.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:52:34.757606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5683f0b7-7982-4c7f-b9d8-b49d6df2948a · outbound

This paper cites an unresolved cited work.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:52:34.583030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 0a7a2b33-6c0b-4035-95e0-88ca5713d675 · outbound

This paper cites an unresolved cited work.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:52:34.361946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b05f372e-61a6-498d-b170-e44eba8543ec · outbound

This paper cites Zhang, J.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Zhang, J

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:34.194150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 41e03925-d0de-4d4f-a0b8-b4be454cfa93 · outbound

This paper cites Zhou and N.

Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise Zhou and N

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:52:34.009945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation 94932a67-7ea4-406e-93a7-9de35aa26b0a · inbound

A splitting mixed finite element method for a stochastic Keller-Segel system with multiplicative noise cites this paper.

A splitting mixed finite element method for a stochastic Keller-Segel system with multiplicative noise Analysis of fully discrete Crank-Nicolson finite element methods for a stochastic Keller-Segel chemotaxis system with gradient-type multiplicative noise

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-11T04:18:41.320808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.