Paper Citation Record · LEDGER

Neural optimization of the most probable paths of 3D active Brownian particles

As of 21 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 2 inbound Pith citation observations for arXiv:2511.16178.

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

pith.paper-citation-record.v1
2511.16178 v3

Coverage vector

measured 51 of 51 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-03T21:15:05.426156Z

measured 53 of 53 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T15:42:03.737026Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T20:21:09.124624Z

Reference resolution

51 of 51 outbound references displayed

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Outbound references

Observation 96bfc405-5621-48ae-9d76-ebf8f2c3cfaf · outbound

This paper cites Lauga,The Fluid Dynamics of Cell Motility(Cambridge Uni- versity Press, Cambridge, 2020).

Neural optimization of the most probable paths of 3D active Brownian particles Lauga,The Fluid Dynamics of Cell Motility(Cambridge Uni- versity Press, Cambridge, 2020)

Reference 1

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Observation 5b35ef9d-2e88-4a1f-a96a-4123398e5179 · outbound

This paper cites Gompper, R.

Neural optimization of the most probable paths of 3D active Brownian particles Gompper, R

Reference 2

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Observation c551272c-36f1-4f05-b1ff-937cfda4a858 · outbound

This paper cites Romanczuk, M.

Neural optimization of the most probable paths of 3D active Brownian particles Romanczuk, M

Reference 3

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Observation f5045fd4-e1d8-4d3e-933e-f66d885eb4bd · outbound

This paper cites Fily and M.

Neural optimization of the most probable paths of 3D active Brownian particles Fily and M

Reference 4

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Observation 993bdf0d-94d6-4352-afdc-eb9c3c9c391f · outbound

This paper cites an unresolved cited work.

Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

Reference 5

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Observation 0f39a487-5a3d-4d61-96f4-cdea33fef7ae · outbound

This paper cites Yasuda, and K.

Neural optimization of the most probable paths of 3D active Brownian particles Yasuda, and K

Reference 6

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Observation ab0a258a-6efd-46e6-8675-2cdd1ec93908 · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

Reference 7

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Observation f47294bd-2cb9-4b75-b948-0a052c779ce7 · outbound

This paper cites Crisanti and M.

Neural optimization of the most probable paths of 3D active Brownian particles Crisanti and M

Reference 8

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Observation 9330464f-99a2-4f39-bcea-795170e435c9 · outbound

This paper cites Dutta, Most probable paths for active Ornstein-Uhlenbeck particles, Phys.

Neural optimization of the most probable paths of 3D active Brownian particles Dutta, Most probable paths for active Ornstein-Uhlenbeck particles, Phys

Reference 9

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Observation f95b445a-122f-4051-be7b-816b0de06165 · outbound

This paper cites Onsager and S.

Neural optimization of the most probable paths of 3D active Brownian particles Onsager and S

Reference 10

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Observation c6dcd761-d3fa-43db-806d-b7ecef975512 · outbound

This paper cites Machlup and L.

Neural optimization of the most probable paths of 3D active Brownian particles Machlup and L

Reference 11

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Observation cf59bcf4-935c-4618-861d-6413835d379e · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

Reference 12

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Observation 132aaad2-33b1-472a-83c3-2790ee8ca11b · outbound

This paper cites Doi, Onsager’s variational principle in soft matter, J.

Neural optimization of the most probable paths of 3D active Brownian particles Doi, Onsager’s variational principle in soft matter, J

Reference 13

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Observation 7f78aecc-7a1f-4344-9e28-5b69bbfbcdd4 · outbound

This paper cites Doi,Soft Matter Physics(Oxford University Press, Oxford, England, 2013).

Neural optimization of the most probable paths of 3D active Brownian particles Doi,Soft Matter Physics(Oxford University Press, Oxford, England, 2013)

Reference 14

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Observation fca74a8f-2271-4f04-b893-a87bc16900a8 · outbound

This paper cites Onsager, Reciprocal relations in irreversible processes.

Neural optimization of the most probable paths of 3D active Brownian particles Onsager, Reciprocal relations in irreversible processes

Reference 15

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Observation bcd07e02-3a06-4c42-8248-a78a4c72abe0 · outbound

This paper cites Onsager, Reciprocal relations in irreversible processes.

Neural optimization of the most probable paths of 3D active Brownian particles Onsager, Reciprocal relations in irreversible processes

Reference 16

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Observation 7f5808ed-6056-42d3-a9e6-fbd4edeb4c75 · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

Reference 17

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Observation 85317f6d-f339-4ca8-bf2b-6b4cf0579aac · outbound

This paper cites Okamoto, Y.

Neural optimization of the most probable paths of 3D active Brownian particles Okamoto, Y

Reference 18

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Observation 8a3e9b30-7177-433d-9f42-3cf21ff20efd · outbound

This paper cites Man and M.

Neural optimization of the most probable paths of 3D active Brownian particles Man and M

Reference 19

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Observation 0ee6914b-49d8-4079-b573-2d061cb8d933 · outbound

This paper cites Zhou and M.

Neural optimization of the most probable paths of 3D active Brownian particles Zhou and M

Reference 20

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Observation 7a3bd519-0829-4101-96c4-231498471082 · outbound

This paper cites Doi, Onsager principle in polymer dynamics, Prog.

Neural optimization of the most probable paths of 3D active Brownian particles Doi, Onsager principle in polymer dynamics, Prog

Reference 21

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Observation 50ca6d23-4ee7-4939-91f6-8daf121384c6 · outbound

This paper cites Zhang, M.

Neural optimization of the most probable paths of 3D active Brownian particles Zhang, M

Reference 22

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Observation aca86121-6bc9-4aa3-9d43-4e2a896e5d92 · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

Reference 23

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Observation 586a89d8-81aa-4912-89e7-91e673498e67 · outbound

This paper cites Ackermann and M.

Neural optimization of the most probable paths of 3D active Brownian particles Ackermann and M

Reference 24

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Observation 66164504-cdc3-49d3-b5b0-540fbbc8bb7a · outbound

This paper cites Taniguchi and E.

Neural optimization of the most probable paths of 3D active Brownian particles Taniguchi and E

Reference 25

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Observation 697d12c1-7f70-4ae1-ad83-cb2a8846896e · outbound

This paper cites Taniguchi and E.

Neural optimization of the most probable paths of 3D active Brownian particles Taniguchi and E

Reference 26

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Observation 3898692f-4d53-435d-89ba-a5dade1df97a · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

Reference 27

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Observation db17beec-b5c1-4b2a-a156-07a2e8695399 · outbound

This paper cites Rohanizadegan, H.

Neural optimization of the most probable paths of 3D active Brownian particles Rohanizadegan, H

Reference 28

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Observation 044f1ffd-4e71-4c77-92a2-bd707da92226 · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

Reference 29

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Observation 5b8bec13-db35-4450-81ee-0aae0b5582dc · outbound

This paper cites Colen, M.

Neural optimization of the most probable paths of 3D active Brownian particles Colen, M

Reference 30

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

Reference 31

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Observation edd50707-0b0c-4216-b995-818cfc95a6fb · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

Reference 32

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Observation 846533e1-d25a-4b04-afb4-e0c214d7c1b8 · outbound

This paper cites Rumelhart, G.

Neural optimization of the most probable paths of 3D active Brownian particles Rumelhart, G

Reference 33

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Observation ea15bf8c-b78a-49da-819d-912b145c1f56 · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

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Observation 725a2e2a-b67a-4cff-bd84-c7ae6aba07f5 · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

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Observation f78a1e76-f441-4b01-b7d9-d4312344291f · outbound

This paper cites Orland, Generating transition paths by Langevin bridges, J.

Neural optimization of the most probable paths of 3D active Brownian particles Orland, Generating transition paths by Langevin bridges, J

Reference 36

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Observation fc8391aa-a876-4ead-9ee8-9052481372ac · outbound

This paper cites (3): d dt (˙x−sinθcosϕ)=0, d dt (˙y−sinθsinϕ)=0, d dt (˙z−cosθ)=0, ˙xcosθcosϕ+ ˙ycosθsinϕ− ˙zsinθ− ˙ϕ2 sinθcosθ+ ¨θ=0, ˙xsinϕ− ˙ycosϕ−2 ˙θ ˙ϕcosθ− ¨ϕsinθ=0.

Neural optimization of the most probable paths of 3D active Brownian particles (3): d dt (˙x−sinθcosϕ)=0, d dt (˙y−sinθsinϕ)=0, d dt (˙z−cosθ)=0, ˙xcosθcosϕ+ ˙ycosθsinϕ− ˙zsinθ− ˙ϕ2 sinθcosθ+ ¨θ=0, ˙xsinϕ− ˙ycosϕ−2 ˙θ ˙ϕcosθ− ¨ϕsinθ=0

Reference 37

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Observation ca7726d4-39bb-480c-bba4-1377b5d3a270 · outbound

This paper cites Sekimoto,Stochastic Energetics(Springer, Berlin/Heidelberg, 2010).

Neural optimization of the most probable paths of 3D active Brownian particles Sekimoto,Stochastic Energetics(Springer, Berlin/Heidelberg, 2010)

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Observation d7b19596-c2b8-4214-adbb-9721e2a4c817 · outbound

This paper cites Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep.

Neural optimization of the most probable paths of 3D active Brownian particles Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep

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Observation 9b9795f3-a5f3-438e-a1fc-db9a032d0542 · outbound

This paper cites Audoly and Y.

Neural optimization of the most probable paths of 3D active Brownian particles Audoly and Y

Reference 40

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Observation 11c6bd65-21f6-49c5-91fb-9508fd9f32e5 · outbound

This paper cites Fruchart, R.

Neural optimization of the most probable paths of 3D active Brownian particles Fruchart, R

Reference 41

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Observation 44e1ac0f-5c8e-4b91-9e60-0915b91a4cd1 · outbound

This paper cites Fruchart, C.

Neural optimization of the most probable paths of 3D active Brownian particles Fruchart, C

Reference 42

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Observation 1ee6559a-7174-4ed9-a171-f908465dcb46 · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

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Observation f45a8b4b-ab39-4dc2-8270-c7e1c3426aee · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

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Observation 5d4fda70-3c9a-4818-82c9-118d3e7be1cd · outbound

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Neural optimization of the most probable paths of 3D active Brownian particles Unresolved cited work

Reference 45

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Observation 9372ba79-15ed-4fda-8a65-8f414ab86ab3 · outbound

This paper cites Tateyama, H.

Neural optimization of the most probable paths of 3D active Brownian particles Tateyama, H

Reference 46

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Observation 220e393e-f5c9-40c8-8a4a-fde2ae400f13 · outbound

This paper cites Yasuda, A.

Neural optimization of the most probable paths of 3D active Brownian particles Yasuda, A

Reference 47

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Observation 09baac38-216b-498a-8f2c-4f2ff4f49245 · outbound

This paper cites Yasuda, K.

Neural optimization of the most probable paths of 3D active Brownian particles Yasuda, K

Reference 48

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Observation 14fee819-902b-4e7b-b61b-bf1e583d74cb · outbound

This paper cites Yasuda, Irreversibility of stochastic state transitions in Langevin systems with odd elasticity, Phys.

Neural optimization of the most probable paths of 3D active Brownian particles Yasuda, Irreversibility of stochastic state transitions in Langevin systems with odd elasticity, Phys

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Observation c4044101-907f-4353-a3da-e1ee8a470734 · outbound

This paper cites Yasuda, K.

Neural optimization of the most probable paths of 3D active Brownian particles Yasuda, K

Reference 50

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Observation f2e2138e-5863-4adb-9a58-7ab55ac88283 · outbound

This paper cites Demon's variational principle for informational active matter.

Neural optimization of the most probable paths of 3D active Brownian particles Demon's variational principle for informational active matter

Reference 51

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Pith citing papers

Observation 9a280267-5541-4a47-aaba-bda94eec0bab · inbound

Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics cites this paper.

Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics Neural optimization of the most probable paths of 3D active Brownian particles

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-06-19T17:09:49.758555Z

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Observation 68b446cd-d5c4-49d8-a12f-a2428004ddf5 · inbound

Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics cites this paper.

Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics Neural optimization of the most probable paths of 3D active Brownian particles

Reference 30

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