Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T14:06:06.180405Z
Paper Citation Record · LEDGER
The Keller-Segel model with mass critical exponent
As of 15 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2412.12586.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
41 of 41 outbound references displayed
- verified exact2
- verified fuzzy21
- unresolved18
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 60967662-0f41-4c71-ad53-4bae0fd0881f · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:07.146689Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 46e7654b-4936-4981-ac26-b356ad6f508c · outbound
This paper cites Bian, The aggregation-diffusion equation with energy c ritical exponent, Discrete and Contin- uous Dynamical Systems - B , 29 (2024) 1128-1145.
The Keller-Segel model with mass critical exponent Bian, The aggregation-diffusion equation with energy c ritical exponent, Discrete and Contin- uous Dynamical Systems - B , 29 (2024) 1128-1145
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:07.124782Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 36b75e7f-e606-46fa-883c-0f056dd7031a · outbound
This paper cites Bian, J.- G.
The Keller-Segel model with mass critical exponent Bian, J.- G
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:07.099408Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 0dd6d890-5100-4fec-82cb-840b2fb3ce1c · outbound
This paper cites Bian, J.- G.
The Keller-Segel model with mass critical exponent Bian, J.- G
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:07.073759Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ab0330b3-5153-48ca-aa3a-8a86d79187c9 · outbound
This paper cites Blanchet, J.
The Keller-Segel model with mass critical exponent Blanchet, J
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:07.050547Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 21196020-a03f-406c-a90f-2a0d0b64d97d · outbound
This paper cites Blanchet, J.
The Keller-Segel model with mass critical exponent Blanchet, J
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:07.028389Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 40c5e9f9-f842-449c-a543-742606626320 · outbound
This paper cites Blanchet, J.
The Keller-Segel model with mass critical exponent Blanchet, J
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:07.000844Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9b356907-3ef6-4202-90b0-a05486bbe7f1 · outbound
This paper cites Calvez, J.
The Keller-Segel model with mass critical exponent Calvez, J
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.971151Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 4814f818-0101-41bc-b431-f04e24e728c1 · outbound
This paper cites Calvez, J.
The Keller-Segel model with mass critical exponent Calvez, J
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.946695Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c176d4bb-dd67-4127-9535-da84f7e9ba67 · outbound
This paper cites Calvez, Blow-up, concentration phenomenon and glob al existence for the Keller-Segel model in high dimension, Communications in Partial Differential Equations , 37 (2012) 561-584.
The Keller-Segel model with mass critical exponent Calvez, Blow-up, concentration phenomenon and glob al existence for the Keller-Segel model in high dimension, Communications in Partial Differential Equations , 37 (2012) 561-584
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.927749Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 77b0931f-6769-4d97-ab32-25b17536f411 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.908142Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation da8ec4d1-361f-49b4-b73c-800c2dbdaf1d · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.889594Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 8683c3ce-6787-4a2e-a345-7e8bc09885f0 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.870212Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f9c20381-581e-4ef5-ad5d-79891692ee58 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.852368Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation dc3a3eed-e57e-45ed-920f-f0ac6621a7fe · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.835216Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 9f1d99c1-f4ae-4f93-a556-3d4e494eab19 · outbound
This paper cites Frisch, S.
The Keller-Segel model with mass critical exponent Frisch, S
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.814389Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c8fffc18-cbad-421b-a341-167d8fec53e9 · outbound
This paper cites Jara, Nonequilibrium scaling limit for a tagged part icle in the simple exclusion process with long jumps, Communications on Pure and Applied Mathematics , (2009).
The Keller-Segel model with mass critical exponent Jara, Nonequilibrium scaling limit for a tagged part icle in the simple exclusion process with long jumps, Communications on Pure and Applied Mathematics , (2009)
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.789038Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 5ea5a3e1-a150-4a7a-b2a9-1df3bda717f2 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.765961Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 058735bc-653e-4155-95e4-951590f7e734 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.745347Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 57fb18f0-c654-4cb1-862c-050c540aa183 · outbound
This paper cites Li, J.-G.
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.725795Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 5b80cdba-5375-43bd-8829-fac612e5dc08 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.703582Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 5761b3a1-dc2b-432c-ac81-c3bf467c01c0 · outbound
This paper cites Mellet, S.
The Keller-Segel model with mass critical exponent Mellet, S
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.676955Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation b567d33a-0690-4d88-8dcb-09fb6fd30ef9 · outbound
This paper cites Perthame, Transport Equations in Biology, Basel-Boston-Berlin: Birkhaeuser Verlag , (2007).
The Keller-Segel model with mass critical exponent Perthame, Transport Equations in Biology, Basel-Boston-Berlin: Birkhaeuser Verlag , (2007)
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.653649Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 0ddf3f74-cc95-4a21-b825-af3047d47ae4 · outbound
This paper cites Sugiyama, Y.
The Keller-Segel model with mass critical exponent Sugiyama, Y
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.632134Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 6f45c04f-8de0-4609-93dc-59b301b6236b · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.612796Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 1b0c42f8-daf0-4cba-a803-c536cf745fad · outbound
This paper cites Sugiyama, H.
The Keller-Segel model with mass critical exponent Sugiyama, H
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.590084Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 5a166e0f-7bbf-48ae-b4d0-1c0f2f40252c · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.563503Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f9390adb-6de4-4711-990f-c5fee2105125 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.540390Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f4e188eb-6405-490f-8231-1be8fc3a1e09 · outbound
This paper cites Baleanu, New applications of fractional variationa l principles, Reports on Mathematical Physics, 61 (2008) 199-206.
The Keller-Segel model with mass critical exponent Baleanu, New applications of fractional variationa l principles, Reports on Mathematical Physics, 61 (2008) 199-206
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.520209Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation a244eae5-3fa8-4275-885c-44cfa811da49 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.495504Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 2f20d655-a167-4fe1-a2a3-444a987f74b8 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.468848Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 8d02125b-bd20-4cb5-ba8c-16a555d07e3f · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.448397Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 6f35302e-2586-42ce-bb22-02dbcac98826 · outbound
This paper cites Liouville type theorems, a priori estimates and existence of solutions for critical order Hardy-H\'{e}non equations in $\mathbb{R}^{n}$.
The Keller-Segel model with mass critical exponent Liouville type theorems, a priori estimates and existence of solutions for critical order Hardy-H\'{e}non equations in $\mathbb{R}^{n}$
Reference 33
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T14:06:06.264366Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation eec8c7f9-1489-4c79-b1c1-04642040a644 · outbound
This paper cites Caffarelli, B.
The Keller-Segel model with mass critical exponent Caffarelli, B
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.423787Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 88e0892b-896b-4729-afa5-15a1d3ff9a6f · outbound
This paper cites Cheng and S.
The Keller-Segel model with mass critical exponent Cheng and S
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.397176Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation cdd10531-0c4c-425e-804b-0fef114a9ea2 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.368751Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation fcbe38d0-bdf8-4fa3-b390-4ad649fe5769 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.343690Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 4ae12756-a7c5-4507-ad4c-0bfdf2c54532 · outbound
This paper cites an unresolved cited work.
The Keller-Segel model with mass critical exponent Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T14:06:06.323781Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation cb073103-6bfa-426e-a03e-0b4106ac4289 · outbound
This paper cites Liouville type theorems, a priori estimates and existence of solutions for non-critical higher order Lane-Emden-Hardy equations.
The Keller-Segel model with mass critical exponent Liouville type theorems, a priori estimates and existence of solutions for non-critical higher order Lane-Emden-Hardy equations
Reference 39
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T14:06:06.234732Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 54696c76-ed8f-43e4-a0fd-25bcfe2cb9b2 · outbound
This paper cites Gidas and J.
The Keller-Segel model with mass critical exponent Gidas and J
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.305453Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 00ef7f11-afbb-49c0-a0eb-aa5427ccb7ed · outbound
This paper cites Wei and X.
The Keller-Segel model with mass critical exponent Wei and X
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T14:06:06.285631Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Pith citing papers
No inbound Pith citation observations are available.