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Paper Citation Record · LEDGER

Learning the Optimal Hydrodynamic Closure

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.

pith.paper-citation-record.v1
2501.13938 v3

Coverage vector

measured 62 of 62 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T19:42:53.415699Z

measured 63 of 63 standing notices

One-hop event checks from named stored sources.

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:16:38.416749Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-15T19:16:38.651258Z

Reference resolution

62 of 62 outbound references displayed

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External citation measurements

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Outbound references

Observation e8e82bff-b161-47d2-9b90-0d5108301630 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 1

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 324567b9-75fb-415f-a70e-552a75cdc103 · outbound

This paper cites The analytic closure serves as a further benchmark to ensure the accuracy of the learned closure up to the cirtical wave number.

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

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 47842ba1-3235-4f93-bdfd-24009dcc614f · outbound

This paper cites As a further illustration of the optimality of the spec- trally closed hydrodynamics, we compute the time evolu- tion of density and temperature directly.

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

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Observation 5b898c8c-b70e-41d1-b3c1-aa9308cf2106 · outbound

This paper cites 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).

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

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 718134fa-131d-4d66-a7db-45437a466178 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 5

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation f4cba4aa-7e2f-4849-8e50-798c4cfd3b37 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 6

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation cac10653-06dc-431a-9aa4-6352b9b7f8ab · outbound

This paper cites Akhlaghi, E.

Learning the Optimal Hydrodynamic Closure Akhlaghi, E

Reference 7

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation f1ca80ec-be91-45d7-985d-a86a075fefff · outbound

This paper cites Bird,Molecular Gas Dynamics and the Direct Simu- lation of Gas Flows(Clarendon Press, 1994).

Learning the Optimal Hydrodynamic Closure Bird,Molecular Gas Dynamics and the Direct Simu- lation of Gas Flows(Clarendon Press, 1994)

Reference 8

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Observation e5e8ff93-e01b-4813-a523-456816521e00 · outbound

This paper cites Jenny, M.

Learning the Optimal Hydrodynamic Closure Jenny, M

Reference 9

Resolution
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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 0617dacf-a3f1-490a-b1b5-f5d869ed622e · outbound

This paper cites Shakhov, Generalization of the Krook kinetic relax- ation equation, Fluid dynamics3, 95 (1968).

Learning the Optimal Hydrodynamic Closure Shakhov, Generalization of the Krook kinetic relax- ation equation, Fluid dynamics3, 95 (1968)

Reference 10

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation faf37b4a-ffa8-4d2d-87c0-e6eab8dc64d5 · outbound

This paper cites Struchtrup and M.

Learning the Optimal Hydrodynamic Closure Struchtrup and M

Reference 11

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation cc340329-8782-4d6d-b522-7e7292bf6ef8 · outbound

This paper cites Wu and X.-J.

Learning the Optimal Hydrodynamic Closure Wu and X.-J

Reference 12

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation a6267cb4-7a2b-481d-8fdf-9b5dfd0ca01c · outbound

This paper cites Zwanzig,Nonequilibrium statistical mechanics(Ox- ford university press, 2001).

Learning the Optimal Hydrodynamic Closure Zwanzig,Nonequilibrium statistical mechanics(Ox- ford university press, 2001)

Reference 13

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unresolved
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Unavailable: canonical work link unavailable.

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Observation 77955e60-a313-47b9-b74c-ad898bbdd057 · outbound

This paper cites Hilbert, Mathematical problems, Bulletin of American Mathematical Society37, 407 (2000).

Learning the Optimal Hydrodynamic Closure Hilbert, Mathematical problems, Bulletin of American Mathematical Society37, 407 (2000)

Reference 14

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Observation 3fed9402-1f35-44a7-a828-17591f7ba753 · outbound

This paper cites Saint-Raymond,Hydrodynamic limits of the Boltz- mann equation, 1971 (Springer Science & Business Me- dia, 2009).

Learning the Optimal Hydrodynamic Closure Saint-Raymond,Hydrodynamic limits of the Boltz- mann equation, 1971 (Springer Science & Business Me- dia, 2009)

Reference 15

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation f28e4378-d1ab-485e-a66c-69a8b1dc0af3 · outbound

This paper cites Chapman and T.

Learning the Optimal Hydrodynamic Closure Chapman and T

Reference 16

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 38afaa22-5103-4d21-90ab-0b394b844555 · outbound

This paper cites Grad, On the kinetic theory of rarefied gases, Commu- nications on pure and applied mathematics2, 331 (1949).

Learning the Optimal Hydrodynamic Closure Grad, On the kinetic theory of rarefied gases, Commu- nications on pure and applied mathematics2, 331 (1949)

Reference 17

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Observation 1735d56f-0ebe-433a-9781-6b1a7380d9b8 · outbound

This paper cites Burnett, The distribution of velocities in a slightly non-uniform gas, Proceedings of the London Mathemat- ical Society2, 385 (1935).

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

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Observation 7f3b4e94-d637-4222-9f72-5c4fc709baf6 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 19

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Observation 8a758fca-75d6-4533-85e3-c88417d073cf · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 20

Resolution
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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 0722bc53-4ceb-4b34-b5fd-413957feff7f · outbound

This paper cites Slemrod, From Boltzmann to Euler: Hilbert’s 6th problem revisited, Computers & Mathematics with Ap- plications65, 1497 (2013), Grasping Complexity.

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

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Observation 4b8553f0-7a48-4a47-af5a-a4dfaebbfcb3 · outbound

This paper cites On the Relation of Exact Hydrodynamics to the Chapman-Enskog Series.

Learning the Optimal Hydrodynamic Closure On the Relation of Exact Hydrodynamics to the Chapman-Enskog Series

Reference 22

Resolution
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Observation 2e9925b7-e2c8-4142-9198-23a21daaadaf · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 23

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Observation e147b97e-fb04-44df-820c-2840c9b13ffd · outbound

This paper cites Gorban and I.

Learning the Optimal Hydrodynamic Closure Gorban and I

Reference 24

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This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 25

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Observation b9fc3556-edd2-4269-8025-b3fa274f1a2f · outbound

This paper cites MacKay, Slow manifolds, inEnergy localisation and Transfer(World Scientific, 2004) pp.

Learning the Optimal Hydrodynamic Closure MacKay, Slow manifolds, inEnergy localisation and Transfer(World Scientific, 2004) pp

Reference 26

Resolution
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Observation 9cff62d3-2250-4ec4-8a1f-16eb8a3f1cd3 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 27

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Observation 78855d68-3fc2-4c4c-a219-ee50e1ce06f1 · outbound

This paper cites Ax ˚ as, M.

Learning the Optimal Hydrodynamic Closure Ax ˚ as, M

Reference 28

Resolution
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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation cc5f64c7-0a63-4725-94ca-dffabe763439 · outbound

This paper cites Fenichel, Geometric singular perturbation theory for ordinary differential equations, Journal of differential equations31, 53 (1979).

Learning the Optimal Hydrodynamic Closure Fenichel, Geometric singular perturbation theory for ordinary differential equations, Journal of differential equations31, 53 (1979)

Reference 29

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 901370e4-aabd-46b2-b888-b11bdc75df4a · outbound

This paper cites de La Llave, Invariant manifolds associated to nonres- onant spectral subspaces, Journal of statistical physics 87, 211 (1997).

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

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 7d642e27-7c3d-4eb4-94c0-3e0af4e11b63 · outbound

This paper cites Cabr´ e, E.

Learning the Optimal Hydrodynamic Closure Cabr´ e, E

Reference 31

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 8e3fc8e8-92e1-47bb-aab9-6d5d2a8f44a9 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 32

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 009a5bf1-8d73-4297-8cca-d517140709d2 · outbound

This paper cites Kogelbauer and I.

Learning the Optimal Hydrodynamic Closure Kogelbauer and I

Reference 33

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 34

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 2099b911-5576-4342-9d93-ead5d2a3bad9 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 35

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation faf895db-8714-44ca-82e6-543cf82f9b6b · outbound

This paper cites Zheng, Y.

Learning the Optimal Hydrodynamic Closure Zheng, Y

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T19:42:53.783394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.312688Z digest=sha256:b7bcf34cff677019aec26f1b09bd0499cb2b670af8de94bef57aa0f34740877e

Observation efecdc2d-d990-4b04-9ee0-62811837a6f1 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 37

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.771591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.316289Z digest=sha256:22941cc16e85966e1e2a950252674e53271a2bd6c766795cfebda5e4ba5e2146

Observation 4754ab93-f992-420f-80f9-df15c794fd60 · outbound

This paper cites Raissi, P.

Learning the Optimal Hydrodynamic Closure Raissi, P

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T19:42:53.759657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.320038Z digest=sha256:f66701f4abf4cb8dd5442c98e40badbd334a14dfa115fa4a7f4edf05309f62c5

Observation 30bc37ea-a9eb-4c45-a698-54a1533df5df · outbound

This paper cites Cercignani,The Boltzmann Equation(Springer New York, 1988).

Learning the Optimal Hydrodynamic Closure Cercignani,The Boltzmann Equation(Springer New York, 1988)

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T19:42:53.748177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.323637Z digest=sha256:d7ade0330037fe9aee3b0f7a471a8ef18795eaa5dabaff170a85c7318fa70d5a

Observation 3740c7c8-97c5-4dc3-84d7-3bb8a0f22fb7 · outbound

This paper cites Risken,The Fokker–Planck Equation(Springer New York, 1996).

Learning the Optimal Hydrodynamic Closure Risken,The Fokker–Planck Equation(Springer New York, 1996)

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T19:42:53.735861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.327649Z digest=sha256:cf6becdaa1f2d20562ab7fa741e7dea9f2f14aee2979a1d81ba1dc865da5c556

Observation 00e8b482-2ce4-4efd-b1a9-efed76513ccf · outbound

This paper cites Kogelbauer and I.

Learning the Optimal Hydrodynamic Closure Kogelbauer and I

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T19:42:53.724071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.331307Z digest=sha256:564ad0be149696da90aebba0670489ef98a29b7962d01140e382186600910287

Observation 864f80cd-c04b-4a0d-b613-70db825216c4 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.713199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.335087Z digest=sha256:6a8c6a9c8b2e1243dc96ea387af05ec2d23059cbc694c47bd455e22a9e112dd4

Observation c3ceba7e-919b-4d4e-9315-dff6848db58d · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.701939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.339332Z digest=sha256:a5688e3eca32cac2dd7ceb3a8f930bf3820c237396b9ba675c92251fc61051f9

Observation ad8db78f-310b-4171-88fc-76d71f6e462c · outbound

This paper cites Karlin, M.

Learning the Optimal Hydrodynamic Closure Karlin, M

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T19:42:53.691012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.343204Z digest=sha256:5b457eb3f2a49354af93b8b9c064a3fccd0cc6c7132380f216a6ed7afc570817

Observation 5f4621d9-cc1c-4748-9979-419a184798d6 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.679506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.347254Z digest=sha256:fc41ee29c83b3645cd732378ff2ffd157fa4fa1ce8f22a83383c65b7091bd2c2

Observation 80a8a89d-cd8c-4d03-968c-7aef00a7394b · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.668381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.351086Z digest=sha256:679e7652cc62072561d2faab1f9e126bc146d719bc6cd36f06c4977116875fc6

Observation cc467ac3-2742-4dbf-b2e6-7175121c0784 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 47

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.656267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.355165Z digest=sha256:a7a2822fd9a7ac134b1f0dcb8a66943b11cdae9883e85a4c8772b2f3e22adf54

Observation 4563a315-4e3d-44cf-87b9-e10aadd56485 · outbound

This paper cites Kogelbauer and I.

Learning the Optimal Hydrodynamic Closure Kogelbauer and I

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T19:42:53.639103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.359536Z digest=sha256:ae0ad2f704d5f19dd156b0d4abeaace452737163a3a9851ff46a8b231e50ba0c

Observation 68988ca1-4e67-43e4-af25-6f027cff53a0 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 49

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.624297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.363513Z digest=sha256:e6229d9511d49b6e219bb1ac2f39061f0fa022971b09253e64495ec51746bef2

Observation 2110127c-f735-42d3-acf6-e958aca55467 · outbound

This paper cites Hansen and I.

Learning the Optimal Hydrodynamic Closure Hansen and I

Reference 50

Resolution
unresolved
no resolver link, observed 2026-08-10T19:42:53.367388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T19:42:53.367388Z digest=sha256:0b7b453d3f67e0481ba255cb016d60e0a012ed5635f15248f6434634baf1916a

Observation 031c9c0a-a70a-4a74-811f-c13a4331df3d · outbound

This paper cites Goodfellow, Y.

Learning the Optimal Hydrodynamic Closure Goodfellow, Y

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T19:42:53.605746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.371668Z digest=sha256:9157e25b2b91b7a265d04773a45fd473810cee7a049b9f525378c2e2ae150d71

Observation 3bd2560b-03a9-4408-a898-7cf03de0764d · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Learning the Optimal Hydrodynamic Closure Adam: A Method for Stochastic Optimization

Reference 52

Resolution
unresolved
no resolver link, observed 2026-08-10T19:42:53.375617Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T19:42:53.375617Z digest=sha256:3b54fef18755fb094c5530df5dc2157fd8b9cbadef714ca156ab4e85061436f7

Observation e73dc1ab-8865-43f7-964e-f3b2316b4289 · outbound

This paper cites Palczewski, Spectral properties of the space nonhomo- geneous linearized Boltzmann operator, Transport The- ory and Statistical Physics13, 409 (1984).

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

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T19:42:53.594774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.379982Z digest=sha256:08c118ca6966eca1821a94546ec9d8651ec301a0209da95d0868d1da5bcb2f8a

Observation 4620e53f-b977-4b6b-b244-d36ecd087cd0 · outbound

This paper cites Wiener, Generalized harmonic analysis, Acta mathe- matica55, 117 (1930).

Learning the Optimal Hydrodynamic Closure Wiener, Generalized harmonic analysis, Acta mathe- matica55, 117 (1930)

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T19:42:53.583344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.383683Z digest=sha256:b15a5c6488fce86d1497f947b158a3aea632833ce1b4b676ecd6bd3782716fad

Observation dc4ada56-5906-4440-a0ca-d4512f9e7b3e · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 55

Resolution
unresolved
no resolver link, observed 2026-08-10T19:42:53.387657Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T19:42:53.387657Z digest=sha256:9188f580fbafb8c67cfaf43b718013fc2f17d00f138f6a058b5ea4fe2e78c54b

Observation bd2dac3b-b7d1-44c1-b6a8-b612d275c9cd · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 56

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.564994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.391574Z digest=sha256:6151264571be45661c8458a4e7ce138efd4846450826f0657a901afc43de06bf

Observation c639e83a-874a-494e-9760-47ecc6e1f9e3 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 57

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.551987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.395246Z digest=sha256:9c88ef3d6103017df23aaae3c534ddc2492c7ae035232d9dd01e489af5e19afb

Observation e14dd4d6-cc07-4ad8-bd02-d3bc3348d9c9 · outbound

This paper cites Spectral Closure for the Linear Boltzmann-BGK Equation.

Learning the Optimal Hydrodynamic Closure Spectral Closure for the Linear Boltzmann-BGK Equation

Reference 58

Resolution
verified exact
local_arxiv, observed 2026-08-10T19:42:53.469424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.399077Z digest=sha256:e94eb8eeeb2818a39ecbfa528940f320ef9e191986b4b442bd3523c5d0797229

Observation d5e4011b-85e8-457a-8ae3-1f1b4a387d5b · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 59

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.539529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.404362Z digest=sha256:0ef1b8f1e1bf87ef42ba2dd536d6e82a4fad268dd2a4b78d487865ca0a653ed7

Observation 287b7e8d-fc31-4638-a69b-3ece4e05357c · outbound

This paper cites Parameter-Predicting Network (NetNN) The networkNetNNis defined by a feedforward archi- tecture: •Input:A single scalar input, the wave numberk.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T19:42:53.527495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.408037Z digest=sha256:bf64a067b860291f30a777a5ab7217b9e5b621cdb7a42ecee816934e13be54e3

Observation 7e8d153f-a7e5-4d93-b474-b2054e50f343 · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 61

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.515568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.412088Z digest=sha256:f38aa7a7daeeba0c8e00d8373ab448ac1ab61897ab0b6ffb58f18817c63b89a5

Observation 783ea8a7-b8ef-4632-b992-4c93b3ae119a · outbound

This paper cites an unresolved cited work.

Learning the Optimal Hydrodynamic Closure Unresolved cited work

Reference 62

Resolution
unresolved
raw_fallback, observed 2026-08-10T19:42:53.504490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-10T19:42:53.415699Z digest=sha256:28a62f897f2313d636556e86a26745b47636fef937108515f4ea8dc128e1f733

Pith citing papers

Observation c824684d-55e5-4d3a-a9f2-4c1bf735a939 · inbound

On the Relation of Exact Hydrodynamics to the Chapman-Enskog Series cites this paper.

On the Relation of Exact Hydrodynamics to the Chapman-Enskog Series Learning the Optimal Hydrodynamic Closure

Reference 29

Resolution
verified exact
local_arxiv, observed 2026-08-15T19:16:38.661523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T19:16:38.416749Z digest=sha256:21b19dccf26dfbef34942786c6a96baf4c348e3e81ae54883de7ab42c3deafa9