Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T11:18:39.240235Z
Paper Citation Record · LEDGER
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis
As of 8 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2506.03351.
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 2026-08-08T06:32:00.761636+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
12 of 12 outbound references displayed
- verified exact0
- verified fuzzy12
- unresolved0
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 665c3bd0-c249-4ad2-a8be-52fe772874c4 · outbound
This paper cites Singular perturbation of differential integral equations describing biased random walks.Journal für die reine und angewandte Mathematik, 322:15–41, 1981.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis Singular perturbation of differential integral equations describing biased random walks.Journal für die reine und angewandte Mathematik, 322:15–41, 1981
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:42.039816Z
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 efd27486-1d48-40b6-b296-e8aa6f8d4959 · outbound
This paper cites Boundary conditions for fractional diffusion.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis Boundary conditions for fractional diffusion
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:41.832123Z
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 d6789d50-bff0-42c3-99d7-733bc9273dfb · outbound
This paper cites Fractional partial differential equations with boundary conditions.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis Fractional partial differential equations with boundary conditions
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:41.581395Z
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 cce9901d-88ab-4808-8ae9-1367ee415475 · outbound
This paper cites Nuclear reactor theory.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis Nuclear reactor theory
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:41.357694Z
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 ed02ae75-a9b8-4c49-9b4f-4cf1c68f948d · outbound
This paper cites Neutron transport theory.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis Neutron transport theory
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:41.103775Z
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 f248a342-2933-4930-ba9c-0fb4fefce629 · outbound
This paper cites Interacting particles with lévy strate- gies: limits of transport equations for swarm robotic systems.SIAM Journal on Applied Mathematics, 80(1):476–498, 2020.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis Interacting particles with lévy strate- gies: limits of transport equations for swarm robotic systems.SIAM Journal on Applied Mathematics, 80(1):476–498, 2020
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:40.907431Z
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 b0967bcb-4157-4911-b279-a069aa5b630d · outbound
This paper cites Fractional Patlak– Keller–Segel equations for chemotactic superdiffusion.SIAM Journal on Applied Math- ematics, 78(2):1155–1173, 2018.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis Fractional Patlak– Keller–Segel equations for chemotactic superdiffusion.SIAM Journal on Applied Math- ematics, 78(2):1155–1173, 2018
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:40.623469Z
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 86d71d0d-df5a-41ba-ae4a-f8987c06b964 · outbound
This paper cites Initiation of slime mold aggregation viewed as an instability.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis Initiation of slime mold aggregation viewed as an instability
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:40.377925Z
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 9f3fefd5-d066-49e4-967d-923eea89a1a9 · outbound
This paper cites From molecular noise to behavioural variability in a single bacterium.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis From molecular noise to behavioural variability in a single bacterium
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:40.125995Z
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 b3749e0b-9b5d-422e-98c3-0be85d9a973b · outbound
This paper cites Asymptotic theory of the linear transport equation for small mean free paths.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis Asymptotic theory of the linear transport equation for small mean free paths
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:39.912426Z
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 f3b12f2d-34b3-470d-a90b-e09d572346da · outbound
This paper cites Persistent cell motion in the absence of external signals: a search strategy for eukaryotic cells.PLoS One, 3(5):e2093, 2008.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis Persistent cell motion in the absence of external signals: a search strategy for eukaryotic cells.PLoS One, 3(5):e2093, 2008
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:39.687719Z
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 17f33311-5836-4886-b421-2ccc10ab4f1e · outbound
This paper cites An asymptotically compat- ible approach for neumann-type boundary condition on nonlocal problems.ESAIM: Mathematical Modelling and Numerical Analysis, 54(4):1373–1413, 2020.
Macroscopic boundary conditions for a fractional diffusion equation in chemotaxis An asymptotically compat- ible approach for neumann-type boundary condition on nonlocal problems.ESAIM: Mathematical Modelling and Numerical Analysis, 54(4):1373–1413, 2020
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:39.489323Z
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.