Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T19:42:53.415699Z
Paper Citation Record · LEDGER
As of 18 August 2026, this Paper Citation Record lists 62 of 62 outbound references and 1 inbound Pith citation observation for arXiv:2501.13938.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T19:42:53.415699Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-15T19:16:38.416749Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-15T19:16:38.651258Z
62 of 62 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation e8e82bff-b161-47d2-9b90-0d5108301630 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 324567b9-75fb-415f-a70e-552a75cdc103 · outbound
Learning the Optimal Hydrodynamic Closure The analytic closure serves as a further benchmark to ensure the accuracy of the learned closure up to the cirtical wave number
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 47842ba1-3235-4f93-bdfd-24009dcc614f · outbound
Learning the Optimal Hydrodynamic Closure As a further illustration of the optimality of the spec- trally closed hydrodynamics, we compute the time evolu- tion of density and temperature directly
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 5b898c8c-b70e-41d1-b3c1-aa9308cf2106 · outbound
Learning the Optimal Hydrodynamic Closure Karplus, Development of multiscale models for com- plex chemical systems: From h+ h 2 to biomolecules (no- bel lecture)., Angewandte Chemie International Edition 53(2014)
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 718134fa-131d-4d66-a7db-45437a466178 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 5
Source-reported events for the cited work
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Observation f4cba4aa-7e2f-4849-8e50-798c4cfd3b37 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 6
Source-reported events for the cited work
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Observation cac10653-06dc-431a-9aa4-6352b9b7f8ab · outbound
Learning the Optimal Hydrodynamic Closure Akhlaghi, E
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f1ca80ec-be91-45d7-985d-a86a075fefff · outbound
Learning the Optimal Hydrodynamic Closure Bird,Molecular Gas Dynamics and the Direct Simu- lation of Gas Flows(Clarendon Press, 1994)
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e5e8ff93-e01b-4813-a523-456816521e00 · outbound
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 0617dacf-a3f1-490a-b1b5-f5d869ed622e · outbound
Learning the Optimal Hydrodynamic Closure Shakhov, Generalization of the Krook kinetic relax- ation equation, Fluid dynamics3, 95 (1968)
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation faf37b4a-ffa8-4d2d-87c0-e6eab8dc64d5 · outbound
Learning the Optimal Hydrodynamic Closure Struchtrup and M
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cc340329-8782-4d6d-b522-7e7292bf6ef8 · outbound
Learning the Optimal Hydrodynamic Closure Wu and X.-J
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a6267cb4-7a2b-481d-8fdf-9b5dfd0ca01c · outbound
Learning the Optimal Hydrodynamic Closure Zwanzig,Nonequilibrium statistical mechanics(Ox- ford university press, 2001)
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 77955e60-a313-47b9-b74c-ad898bbdd057 · outbound
Learning the Optimal Hydrodynamic Closure Hilbert, Mathematical problems, Bulletin of American Mathematical Society37, 407 (2000)
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3fed9402-1f35-44a7-a828-17591f7ba753 · outbound
Learning the Optimal Hydrodynamic Closure Saint-Raymond,Hydrodynamic limits of the Boltz- mann equation, 1971 (Springer Science & Business Me- dia, 2009)
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f28e4378-d1ab-485e-a66c-69a8b1dc0af3 · outbound
Learning the Optimal Hydrodynamic Closure Chapman and T
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 38afaa22-5103-4d21-90ab-0b394b844555 · outbound
Learning the Optimal Hydrodynamic Closure Grad, On the kinetic theory of rarefied gases, Commu- nications on pure and applied mathematics2, 331 (1949)
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 1735d56f-0ebe-433a-9781-6b1a7380d9b8 · outbound
Learning the Optimal Hydrodynamic Closure Burnett, The distribution of velocities in a slightly non-uniform gas, Proceedings of the London Mathemat- ical Society2, 385 (1935)
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7f3b4e94-d637-4222-9f72-5c4fc709baf6 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 8a758fca-75d6-4533-85e3-c88417d073cf · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 0722bc53-4ceb-4b34-b5fd-413957feff7f · outbound
Learning the Optimal Hydrodynamic Closure Slemrod, From Boltzmann to Euler: Hilbert’s 6th problem revisited, Computers & Mathematics with Ap- plications65, 1497 (2013), Grasping Complexity
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4b8553f0-7a48-4a47-af5a-a4dfaebbfcb3 · outbound
Learning the Optimal Hydrodynamic Closure On the Relation of Exact Hydrodynamics to the Chapman-Enskog Series
Reference 22
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2e9925b7-e2c8-4142-9198-23a21daaadaf · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e147b97e-fb04-44df-820c-2840c9b13ffd · outbound
Learning the Optimal Hydrodynamic Closure Gorban and I
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b2b8029f-5de2-44e8-9469-b50b434ca76b · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b9fc3556-edd2-4269-8025-b3fa274f1a2f · outbound
Learning the Optimal Hydrodynamic Closure MacKay, Slow manifolds, inEnergy localisation and Transfer(World Scientific, 2004) pp
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9cff62d3-2250-4ec4-8a1f-16eb8a3f1cd3 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 78855d68-3fc2-4c4c-a219-ee50e1ce06f1 · outbound
Learning the Optimal Hydrodynamic Closure Ax ˚ as, M
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation cc5f64c7-0a63-4725-94ca-dffabe763439 · outbound
Learning the Optimal Hydrodynamic Closure Fenichel, Geometric singular perturbation theory for ordinary differential equations, Journal of differential equations31, 53 (1979)
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 901370e4-aabd-46b2-b888-b11bdc75df4a · outbound
Learning the Optimal Hydrodynamic Closure de La Llave, Invariant manifolds associated to nonres- onant spectral subspaces, Journal of statistical physics 87, 211 (1997)
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7d642e27-7c3d-4eb4-94c0-3e0af4e11b63 · outbound
Learning the Optimal Hydrodynamic Closure Cabr´ e, E
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 8e3fc8e8-92e1-47bb-aab9-6d5d2a8f44a9 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 009a5bf1-8d73-4297-8cca-d517140709d2 · outbound
Learning the Optimal Hydrodynamic Closure Kogelbauer and I
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b705ff94-27b6-4bc0-83b3-fa92f155833b · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 2099b911-5576-4342-9d93-ead5d2a3bad9 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation faf895db-8714-44ca-82e6-543cf82f9b6b · outbound
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation efecdc2d-d990-4b04-9ee0-62811837a6f1 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4754ab93-f992-420f-80f9-df15c794fd60 · outbound
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 30bc37ea-a9eb-4c45-a698-54a1533df5df · outbound
Learning the Optimal Hydrodynamic Closure Cercignani,The Boltzmann Equation(Springer New York, 1988)
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3740c7c8-97c5-4dc3-84d7-3bb8a0f22fb7 · outbound
Learning the Optimal Hydrodynamic Closure Risken,The Fokker–Planck Equation(Springer New York, 1996)
Reference 40
Source-reported events for the cited work
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Observation 00e8b482-2ce4-4efd-b1a9-efed76513ccf · outbound
Learning the Optimal Hydrodynamic Closure Kogelbauer and I
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 864f80cd-c04b-4a0d-b613-70db825216c4 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c3ceba7e-919b-4d4e-9315-dff6848db58d · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ad8db78f-310b-4171-88fc-76d71f6e462c · outbound
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 5f4621d9-cc1c-4748-9979-419a184798d6 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 80a8a89d-cd8c-4d03-968c-7aef00a7394b · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation cc467ac3-2742-4dbf-b2e6-7175121c0784 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4563a315-4e3d-44cf-87b9-e10aadd56485 · outbound
Learning the Optimal Hydrodynamic Closure Kogelbauer and I
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 68988ca1-4e67-43e4-af25-6f027cff53a0 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 2110127c-f735-42d3-acf6-e958aca55467 · outbound
Learning the Optimal Hydrodynamic Closure Hansen and I
Reference 50
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 031c9c0a-a70a-4a74-811f-c13a4331df3d · outbound
Learning the Optimal Hydrodynamic Closure Goodfellow, Y
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3bd2560b-03a9-4408-a898-7cf03de0764d · outbound
Learning the Optimal Hydrodynamic Closure Adam: A Method for Stochastic Optimization
Reference 52
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e73dc1ab-8865-43f7-964e-f3b2316b4289 · outbound
Learning the Optimal Hydrodynamic Closure Palczewski, Spectral properties of the space nonhomo- geneous linearized Boltzmann operator, Transport The- ory and Statistical Physics13, 409 (1984)
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4620e53f-b977-4b6b-b244-d36ecd087cd0 · outbound
Learning the Optimal Hydrodynamic Closure Wiener, Generalized harmonic analysis, Acta mathe- matica55, 117 (1930)
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation dc4ada56-5906-4440-a0ca-d4512f9e7b3e · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 55
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bd2dac3b-b7d1-44c1-b6a8-b612d275c9cd · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c639e83a-874a-494e-9760-47ecc6e1f9e3 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e14dd4d6-cc07-4ad8-bd02-d3bc3348d9c9 · outbound
Learning the Optimal Hydrodynamic Closure Spectral Closure for the Linear Boltzmann-BGK Equation
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d5e4011b-85e8-457a-8ae3-1f1b4a387d5b · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 287b7e8d-fc31-4638-a69b-3ece4e05357c · outbound
Learning the Optimal Hydrodynamic Closure Parameter-Predicting Network (NetNN) The networkNetNNis defined by a feedforward archi- tecture: •Input:A single scalar input, the wave numberk
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7e8d153f-a7e5-4d93-b474-b2054e50f343 · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 61
Source-reported events for the cited work
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Observation 783ea8a7-b8ef-4632-b992-4c93b3ae119a · outbound
Learning the Optimal Hydrodynamic Closure Unresolved cited work
Reference 62
Source-reported events for the cited work
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Observation c824684d-55e5-4d3a-a9f2-4c1bf735a939 · inbound
On the Relation of Exact Hydrodynamics to the Chapman-Enskog Series Learning the Optimal Hydrodynamic Closure
Reference 29
Source-reported events for the cited work
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