Paper Citation Record · LEDGER

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison

As of 15 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 1 inbound Pith citation observation for arXiv:2505.14278.

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

pith.paper-citation-record.v1
2505.14278 v1

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:47:47.244885Z

measured 46 of 46 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T14:09:10.442564Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T14:09:11.748213Z

Reference resolution

45 of 45 outbound references displayed

verified exact1
verified fuzzy26
unresolved18
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation eed78905-3aa1-44e8-9d93-c2bec7edff87 · outbound

This paper cites 9, 1189–1209.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison 9, 1189–1209

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:55.573632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b2320e36-aedd-4820-be06-cb5560b546a3 · outbound

This paper cites Strauss,Semi-linear second-order elliptic equations in L1, J.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Strauss,Semi-linear second-order elliptic equations in L1, J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:55.286410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 97ca1ffd-5ecb-42e1-8c95-0488944f3f85 · outbound

This paper cites J.63(1991), no.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison J.63(1991), no

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:55.046386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 73034a74-5e82-4be8-9767-57570f161430 · outbound

This paper cites 3, Paper No.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison 3, Paper No

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:54.817910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 1bbd9a6f-6b69-4d17-9366-4309d363a392 · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:47:54.605462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cf872dec-84ae-48e3-bf73-dfb8ffa9d535 · outbound

This paper cites 5, 1057–1076.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison 5, 1057–1076

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:54.416950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 452a4854-2bd2-42cd-b1ad-644cfd9cb989 · outbound

This paper cites Pure Appl.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Pure Appl

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:54.193428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e41101a7-e1ab-4edd-8080-d8518c4a6c64 · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:47:53.865846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 25d3f749-a83d-4861-ad0e-217ec5b9ee1a · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:47:53.626841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e4ce1ac4-d0df-4af3-bda7-2cb5b738cf37 · outbound

This paper cites Differential Equations263(2017), no.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Differential Equations263(2017), no

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:53.307453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a6cc8fa2-a6f8-4a36-827d-152778f79a36 · outbound

This paper cites Differential Equations266(2019), no.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Differential Equations266(2019), no

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:53.170732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b616e6e3-d75c-48fc-b0c5-313f8e254dbe · outbound

This paper cites Herrero and Juan J.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Herrero and Juan J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:52.882899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 96b81774-460c-4860-a8f8-2cad162450db · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T15:47:43.667692Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7fc02cf1-7e3b-4359-b2cd-446423a79a49 · outbound

This paper cites Differential Equations416(2025), 2085–2133.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Differential Equations416(2025), 2085–2133

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:52.713639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8e8baf4c-3c13-4036-95d2-3145c757bf35 · outbound

This paper cites Jäger and S.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Jäger and S

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T15:47:43.865791Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8bc41d2f-aca7-4c0a-8c16-5dea2e7357fb · outbound

This paper cites Keller and Lee A.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Keller and Lee A

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:52.422758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 86a961e7-a33f-4d4b-9a40-726212a77f24 · outbound

This paper cites 10, Paper No.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison 10, Paper No

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:52.237372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f46e7f87-6c08-454e-a082-9959c32dfccf · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:47:52.112459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ea21bea7-006f-495a-a2e5-b37291a4bc44 · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:47:51.982556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c695ed92-5039-4e8b-b44d-bc944b9c20a8 · outbound

This paper cites Macfarlane, Tommaso Lorenzi, and Kevin J.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Macfarlane, Tommaso Lorenzi, and Kevin J

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:51.837298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5a4cdfff-646d-4af9-bcec-e1bae82f172e · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T15:47:44.624893Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8826749-9cf1-48e9-9d29-9d04a3ba5f6e · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 22

Resolution: verified exact; raw_fallback, observed 2026-08-07T15:47:47.815310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation de0528a6-8441-48b0-bfdf-4a98be5329a4 · outbound

This paper cites A note on the $8\pi$ problem of J\"ager-Luckhaus system.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison A note on the $8\pi$ problem of J\"ager-Luckhaus system

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T15:47:44.815694Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 018ddb6b-6377-496d-902f-85d04b29d026 · outbound

This paper cites Finite-time blowup in a fully parabolic chemotaxis model involving indirect signal production.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Finite-time blowup in a fully parabolic chemotaxis model involving indirect signal production

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-07T15:47:44.908004Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47b6daae-4291-4674-809c-f38a7d43416d · outbound

This paper cites 8, 1870–1886.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison 8, 1870–1886

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:51.712837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0d6bea18-35bf-400c-9ba5-65c4ffb960c3 · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:47:51.535650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6001a421-f6b8-4054-aedf-4395b8ba0b7a · outbound

This paper cites Ekvac.40(1997), no.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Ekvac.40(1997), no

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:51.383455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation fd02c2d8-ce6f-4aaa-9758-d5ac6cd28b85 · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T15:47:45.324953Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 173d88cb-f1fb-401c-a3d4-462819dae41b · outbound

This paper cites Painter and Thomas Hillen,Volume-filling and quorum-sensing in models for chemosensitive movement, Can.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Painter and Thomas Hillen,Volume-filling and quorum-sensing in models for chemosensitive movement, Can

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:51.218890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 38cfe931-c80c-4c06-aa86-963d6269a1b8 · outbound

This paper cites Painter and Michael Winkler,Phenotype switching in chemotaxis aggregation models controls the spontaneous emergence of large densities, SIAM J.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Painter and Michael Winkler,Phenotype switching in chemotaxis aggregation models controls the spontaneous emergence of large densities, SIAM J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:51.079565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8734d73e-0652-4ab2-a724-adbf88234d61 · outbound

This paper cites Differential Equations6(2001), no.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Differential Equations6(2001), no

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:50.896560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c20ae272-5490-4a29-8a55-bc070f8a507b · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:47:50.636177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ddf1cad4-c32f-4cc5-b4ed-476d5d911b02 · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:47:50.305183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 21508d7a-4f29-4a9c-90b9-e176b8e905ae · outbound

This paper cites Strohm, R.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Strohm, R

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:50.145775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 76bba5ea-4732-47e5-956a-58ac9cd07015 · outbound

This paper cites Suzuki,Exclusion of boundary blowup for 2D chemotaxis system provided with Dirichlet boundary condition for the Poisson part, J.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Suzuki,Exclusion of boundary blowup for 2D chemotaxis system provided with Dirichlet boundary condition for the Poisson part, J

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-07T15:47:46.114777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb45a88f-cf03-4ce3-8e94-3b65a0f655a6 · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:47:49.956798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 824cc13b-693e-4fc8-9fd8-874c27ecad59 · outbound

This paper cites Differential Equations423(2025), 197–239.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Differential Equations423(2025), 197–239

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:49.784972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3f916e89-5a88-4abb-826f-e93d8d8b4337 · outbound

This paper cites An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis37(2012), no.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis37(2012), no

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:49.515416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9ce8cc59-94c8-4c82-a493-6c22f1cfe75f · outbound

This paper cites Ignacio Tello,Blow up of solutions for a Parabolic-Elliptic chemotaxis system with gradient dependent chemotactic coefficient, Comm.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Ignacio Tello,Blow up of solutions for a Parabolic-Elliptic chemotaxis system with gradient dependent chemotactic coefficient, Comm

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:49.244797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ea27699b-fcf8-4aff-8244-d7b6abaf4596 · outbound

This paper cites global diffusive behavior in the higher-dimensional Keller-Segel model, J.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison global diffusive behavior in the higher-dimensional Keller-Segel model, J

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-07T15:47:46.734766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 586ccec9-812a-423b-b4c7-273eb42baf79 · outbound

This paper cites 5, 2031–2056.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison 5, 2031–2056

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:48.995066Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 60075424-72dc-4009-bf47-0ba26562dee5 · outbound

This paper cites Ann.373(2019), no.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Ann.373(2019), no

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:48.744646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c9b7c828-3d49-44d2-bfd3-1151e6c84ee0 · outbound

This paper cites an unresolved cited work.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:47:48.524861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c35daf47-7a96-4717-9521-cf3fd179c249 · outbound

This paper cites Models Methods Appl.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Models Methods Appl

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:48.275292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8b60a487-e2f9-4e01-9027-df8dfaaa6579 · outbound

This paper cites Djie,Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect, Nonlinear Anal.72(2010), no.

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison Djie,Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect, Nonlinear Anal.72(2010), no

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:47:48.055355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

Observation 6a9e5ffb-2fc5-446e-ba7f-a2f6546b1ef1 · inbound

Mass threshold for global existence in chemotaxis systems with critical flux limitation cites this paper.

Mass threshold for global existence in chemotaxis systems with critical flux limitation Critical mass for finite-time chemotactic collapse in the critical dimension via comparison

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-06T14:09:11.753840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.