Paper Citation Record · LEDGER

Mathematical Models for Fish Schooling

As of 10 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 4 inbound Pith citation observations for arXiv:2508.08310.

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

pith.paper-citation-record.v1
2508.08310 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T22:40:01.351879Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T22:40:01.215612Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-14T21:43:00.508042Z

Reference resolution

34 of 34 outbound references displayed

verified exact2
verified fuzzy20
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 835cee64-03b1-417b-b0af-aab5161efaa2 · outbound

This paper cites Mathematical Models for Fish Schooling.

Mathematical Models for Fish Schooling Mathematical Models for Fish Schooling

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-05T22:40:01.215612Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 81b4d46e-0c24-4e37-addd-3ca15a7d2ebd · outbound

This paper cites In [ 16], we introduced ﬁve components constructing a SDE model for ﬁsh schooling in free space.

Mathematical Models for Fish Schooling In [ 16], we introduced ﬁve components constructing a SDE model for ﬁsh schooling in free space

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.935667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3540ed5e-60e7-46df-9428-e4266d158554 · outbound

This paper cites When two particles i and j are far from each other, both would move toward each other.

Mathematical Models for Fish Schooling When two particles i and j are far from each other, both would move toward each other

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.922705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6b62e45d-6c8c-4e5a-b739-17708c8bf70c · outbound

This paper cites When two particles i and j are close enough, both would move far from each other.

Mathematical Models for Fish Schooling When two particles i and j are close enough, both would move far from each other

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.910031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5d975d55-ed36-4e75-aeb3-0bb90c4a0bce · outbound

This paper cites an unresolved cited work.

Mathematical Models for Fish Schooling Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:01.896376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 10c9f0d9-fba9-498c-8ba1-2242a4c8fa9a · outbound

This paper cites The individual i react to the environment a force Fi(xi, vi).

Mathematical Models for Fish Schooling The individual i react to the environment a force Fi(xi, vi)

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.883257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d68c231a-5710-4169-bdfe-04c9488f0c72 · outbound

This paper cites All particles are subject to random factors or nois e.

Mathematical Models for Fish Schooling All particles are subject to random factors or nois e

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.869499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0381a817-5e02-45fe-b7a1-acbc0d4aac8f · outbound

This paper cites In [ 10], we introduced a ﬁsh schooling model in spaces with ob- stacle.

Mathematical Models for Fish Schooling In [ 10], we introduced a ﬁsh schooling model in spaces with ob- stacle

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.856142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6b9baf5d-1dce-4296-8bd2-bce5a1f779e7 · outbound

This paper cites In this section, we give an example for the model ( 3.3) in two-dimensional space.

Mathematical Models for Fish Schooling In this section, we give an example for the model ( 3.3) in two-dimensional space

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.842492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 41765086-d134-4c45-aa94-36e2a9e0f53b · outbound

This paper cites Aoki, A simulation study on the schooling mechanism in ﬁsh, Bull.

Mathematical Models for Fish Schooling Aoki, A simulation study on the schooling mechanism in ﬁsh, Bull

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.828983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7568cf45-b646-45e5-b291-8e599eb765cb · outbound

This paper cites Camazine, J.

Mathematical Models for Fish Schooling Camazine, J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.815501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 90ae5965-a37d-45b8-9088-043370f937cd · outbound

This paper cites Cucker, E.

Mathematical Models for Fish Schooling Cucker, E

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.803267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 87ac5781-5ff1-4737-aa6e-f6142f4105f4 · outbound

This paper cites Cucker, S.

Mathematical Models for Fish Schooling Cucker, S

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.790783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2485a220-ee77-46ac-921b-7513efbc3f3d · outbound

This paper cites Cucker, S.

Mathematical Models for Fish Schooling Cucker, S

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.777851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1e013d1d-0a1f-44cd-b1df-5064281bf77c · outbound

This paper cites an unresolved cited work.

Mathematical Models for Fish Schooling Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:01.765083Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 533a8acd-179e-45d3-a65e-328ebc602b89 · outbound

This paper cites an unresolved cited work.

Mathematical Models for Fish Schooling Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:01.752033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d87bb831-cace-4b9b-bc18-55a798fd72a3 · outbound

This paper cites A stochastic differential equation model for foraging behavior of fish schools.

Mathematical Models for Fish Schooling A stochastic differential equation model for foraging behavior of fish schools

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-05T22:40:01.423695Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b3a33ad7-d7cf-47e8-aa5e-2f5e5a5a7055 · outbound

This paper cites an unresolved cited work.

Mathematical Models for Fish Schooling Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:01.739517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1dfb1527-449c-41a2-8aab-903a3441eb67 · outbound

This paper cites an unresolved cited work.

Mathematical Models for Fish Schooling Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:01.726340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 987acb40-050a-40ed-8870-6243b6fd608a · outbound

This paper cites Oboshi, S.

Mathematical Models for Fish Schooling Oboshi, S

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.713551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5920158e-6246-4c34-acf9-9e2ebb83f5ca · outbound

This paper cites Olfati-Saber, Flocking for multi-agent dynamic sys tems: Algorithms and Theory, IEEE Trans.

Mathematical Models for Fish Schooling Olfati-Saber, Flocking for multi-agent dynamic sys tems: Algorithms and Theory, IEEE Trans

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.700987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e9723c49-5f30-4216-8021-1576ad9d226e · outbound

This paper cites an unresolved cited work.

Mathematical Models for Fish Schooling Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:01.688130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b36c4f80-2513-41c6-8c5b-b300bf3e2d60 · outbound

This paper cites Shklarsh, G.

Mathematical Models for Fish Schooling Shklarsh, G

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.675350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 38b705e4-497d-4428-9fb9-003681a4bedb · outbound

This paper cites an unresolved cited work.

Mathematical Models for Fish Schooling Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:01.662960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2886828a-2f3b-41e4-a858-a7b4cb8c7606 · outbound

This paper cites Uchitane, T.

Mathematical Models for Fish Schooling Uchitane, T

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.649589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 17774b25-9b80-4fc0-b695-9d5c759f89d3 · outbound

This paper cites Vicsek, A.

Mathematical Models for Fish Schooling Vicsek, A

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.637263Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation aa7908fb-5a45-4fc9-a9a9-e2d19d16cc4f · outbound

This paper cites Zienkiewicz, D.

Mathematical Models for Fish Schooling Zienkiewicz, D

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.623897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 30ba2b55-1536-46e8-a3d1-773f2484a88e · outbound

This paper cites an unresolved cited work.

Mathematical Models for Fish Schooling Unresolved cited work

Reference 28

Resolution: verified exact; doi, observed 2026-08-05T22:40:01.386504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a5b72a46-138f-448b-abef-a6d988754541 · outbound

This paper cites an unresolved cited work.

Mathematical Models for Fish Schooling Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:01.609119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f112aed5-f324-4f65-9a2f-cb694f0ef89b · outbound

This paper cites an unresolved cited work.

Mathematical Models for Fish Schooling Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:01.595922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d6da80e7-3339-4047-8774-4b6a85d5e6f8 · outbound

This paper cites Math-for-Industry.

Mathematical Models for Fish Schooling Math-for-Industry

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.477871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation cf220f9f-1d75-4d58-9ab3-59f6380597ae · outbound

This paper cites an unresolved cited work.

Mathematical Models for Fish Schooling Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:40:01.464916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4bd24c04-c044-4b55-91df-5fc36b144d88 · outbound

This paper cites Math-for-Industry.

Mathematical Models for Fish Schooling Math-for-Industry

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:40:01.451840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 45bc3ccd-e6da-4a59-82c7-fc7e14fc2da6 · outbound

This paper cites Quantifying Fish School Fragmentation under Predation Using Stochastic Differential Equations.

Mathematical Models for Fish Schooling Quantifying Fish School Fragmentation under Predation Using Stochastic Differential Equations

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-05T22:40:01.351879Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 835cee64-03b1-417b-b0af-aab5161efaa2 · inbound