Paper Citation Record · LEDGER

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows

As of 5 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 2 inbound Pith citation observations for arXiv:2605.12723.

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

pith.paper-citation-record.v1
2605.12723 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-14T19:54:43.878250Z

measured 38 of 38 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-11T11:50:26.030339Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-11T02:37:46.701191Z

Reference resolution

36 of 36 outbound references displayed

verified exact26
verified fuzzy1
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External citation measurements

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Outbound references

Observation 45b30995-e936-4188-9643-19430b3aaead · outbound

This paper cites Numerical modeling of axisymmetric and three-dimensional flows in microelec- tromechanical systems nozzles.AIAA journal, 40(5), 897–904 (2002).

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Numerical modeling of axisymmetric and three-dimensional flows in microelec- tromechanical systems nozzles.AIAA journal, 40(5), 897–904 (2002)

Reference 1

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.815931Z

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Observation 6eb80591-4b7d-41d0-b6c8-5351f285bbfd · outbound

This paper cites doi: 10.1016/j.ast.2015.07.016.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows doi: 10.1016/j.ast.2015.07.016

Reference 2

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.720931Z

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Observation 83b15536-5ce4-4639-acd7-5706d5280fc8 · outbound

This paper cites Numericalandexperimentalinvestigationofrarefiedhypersonicflowinanozzle.PhysicsofFluids, 36(11), 116131 (2024).

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Numericalandexperimentalinvestigationofrarefiedhypersonicflowinanozzle.PhysicsofFluids, 36(11), 116131 (2024)

Reference 3

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.696843Z

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Observation e832981a-d57f-469f-b228-c497e97a8c10 · outbound

This paper cites Numerical investigation of micropropulsion systems for CubeSats: Gas species and geometrical effects on nozzle performance.Aerospace Science and Technology, 155, 109625 (2024).

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Numerical investigation of micropropulsion systems for CubeSats: Gas species and geometrical effects on nozzle performance.Aerospace Science and Technology, 155, 109625 (2024)

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:57:52.779783Z

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Observation 298fb566-afc1-4658-8e1e-a278fb7e1c85 · outbound

This paper cites Numerical Study of Facility Pressure Effects on Micronozzles for Space Propulsion.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Numerical Study of Facility Pressure Effects on Micronozzles for Space Propulsion

Reference 5

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.760607Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 5a5a333d-7fd6-40eb-8cd2-bf44b35fad89 · outbound

This paper cites Propulsive performance of micro-nozzlesworkingwithnoblegasmixturesandexpandingintovacuum.JournaloftheBrazilian Society of Mechanical Sciences and Engineering, 47(3), 134 (2025).

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Propulsive performance of micro-nozzlesworkingwithnoblegasmixturesandexpandingintovacuum.JournaloftheBrazilian Society of Mechanical Sciences and Engineering, 47(3), 134 (2025)

Reference 6

Resolution: malformed identifier; doi_truncated, observed 2026-05-14T19:57:52.772994Z

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Observation c4deacf7-f00a-413b-b625-3df2911db67d · outbound

This paper cites Plume–Plume and Plume–Surface Interactions of Micronozzle Clusters in Vacuum.AIAA Journal, 1–26 (2025).

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Plume–Plume and Plume–Surface Interactions of Micronozzle Clusters in Vacuum.AIAA Journal, 1–26 (2025)

Reference 7

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.649400Z

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Observation 124be54b-5ba4-4ef9-8da5-6d5bcbd1f2cf · outbound

This paper cites Oxford Univer- sity Press (2018).https://doi.org/10.1093/oso/9780198814788.001.0001.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Oxford Univer- sity Press (2018).https://doi.org/10.1093/oso/9780198814788.001.0001

Reference 8

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Observation 74f24760-8372-44ee-93d0-bc95affff264 · outbound

This paper cites an unresolved cited work.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-05-15T17:21:22.327014Z

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Observation a133bb8d-5b2d-4325-85e6-dcdd501ecbfc · outbound

This paper cites Microflu- idics and Nanofluidics 10, 321–335.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Microflu- idics and Nanofluidics 10, 321–335

Reference 10

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.672029Z

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Observation ccc8d83b-6095-4728-a430-32d9d4176092 · outbound

This paper cites doi: 10.1103/PhysRevFluids.1.083402.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows doi: 10.1103/PhysRevFluids.1.083402

Reference 11

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.784519Z

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Observation c5c6ed20-6434-493a-b291-0edd4b211733 · outbound

This paper cites Effectofbulkviscosityandrelaxationmodelonnonequilibriumshockstructureofdiatomicgases.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Effectofbulkviscosityandrelaxationmodelonnonequilibriumshockstructureofdiatomicgases

Reference 12

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.641305Z

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Observation bd56742e-08b1-41fb-a92f-cf9c11d90745 · outbound

This paper cites On the basic concepts of the direct simulation monte carlo method.Physics of Fluids, 31(6), 067104 (2019).

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows On the basic concepts of the direct simulation monte carlo method.Physics of Fluids, 31(6), 067104 (2019)

Reference 13

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.755763Z

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Observation d925df8f-4fa7-498b-a9be-c46f353d77a4 · outbound

This paper cites Numerical study of cold gas micronozzleflows.37thaerospacesciencesmeetingandexhibit,166(1999).doi: 10.2514/6.1999- 166.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Numerical study of cold gas micronozzleflows.37thaerospacesciencesmeetingandexhibit,166(1999).doi: 10.2514/6.1999- 166

Reference 14

Resolution: malformed identifier; doi_truncated, observed 2026-05-14T19:57:52.660249Z

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Observation 390b9dbf-4cde-4f35-b61a-c794a061e897 · outbound

This paper cites an unresolved cited work.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Unresolved cited work

Reference 15

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.676429Z

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Observation ad06317d-6189-498f-be08-9d686d5bf828 · outbound

This paper cites Hybrid simulations of rar- efied supersonic gas flows in micro-nozzles.Computers & fluids, 49(1), 312–322 (2011).

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Hybrid simulations of rar- efied supersonic gas flows in micro-nozzles.Computers & fluids, 49(1), 312–322 (2011)

Reference 16

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.789935Z

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Observation 981a2ace-5c5a-43dc-a3f3-9d9f27f365b8 · outbound

This paper cites Sanderse, Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods, Journal of Computational Physics 421 (2020).

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Sanderse, Non-linearly stable reduced-order models for incompressible flow with energy-conserving finite volume methods, Journal of Computational Physics 421 (2020)

Reference 17

Resolution: metadata mismatch; arxiv_id, observed 2026-05-14T19:57:52.667418Z

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Observation 7b95ffaf-1e2e-4f27-86df-a2e9eb832f9a · outbound

This paper cites Boundarycondition- based machine learning algorithm for fast prediction of supersonic flows.Physics of Fluids, 37(8), 086107 (2025).

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Boundarycondition- based machine learning algorithm for fast prediction of supersonic flows.Physics of Fluids, 37(8), 086107 (2025)

Reference 18

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.731482Z

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Observation 81e62b7c-221b-461d-a83a-0a7180f60f5b · outbound

This paper cites and Sahoo, Niranjan.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows and Sahoo, Niranjan

Reference 19

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.735968Z

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Observation 76c7208d-0182-4fae-9723-692176507933 · outbound

This paper cites Tatsios, A.K.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Tatsios, A.K

Reference 20

Resolution: metadata mismatch; arxiv_id, observed 2026-05-14T19:57:52.655611Z

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Observation e06c7d31-74bc-4970-abfa-fa6f4ae2b3cb · outbound

This paper cites Physics-based machine learning closures and wall models for hypersonic transition-continuum boundary layer predictions.Physical Review Fluids, 11(3), 033402 (2026).

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Physics-based machine learning closures and wall models for hypersonic transition-continuum boundary layer predictions.Physical Review Fluids, 11(3), 033402 (2026)

Reference 21

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Observation 2a82f883-f16a-41d7-9ea9-bd111f4d18ca · outbound

This paper cites Neural networks for rarefiedgasdynamics: Relaxationproblem,polyatomicshockwaves,andhypersoniccylinderflow.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Neural networks for rarefiedgasdynamics: Relaxationproblem,polyatomicshockwaves,andhypersoniccylinderflow

Reference 22

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.681313Z

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Observation f129646b-2416-45a1-a4b9-7cc6536e24d9 · outbound

This paper cites Konduri, Charles B.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Konduri, Charles B

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:57:52.796170Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation b36103ba-39a5-4e7b-b35e-ba210533c510 · outbound

This paper cites A Locally enhanced physics-informed neural network surrogate model for rapid aerothermal as- sessment of aero-engine nozzles.Aerospace Science and Technology, 168, 111002 (2026).

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows A Locally enhanced physics-informed neural network surrogate model for rapid aerothermal as- sessment of aero-engine nozzles.Aerospace Science and Technology, 168, 111002 (2026)

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:57:52.750488Z

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Observation 371c85ee-ef77-4fd2-bcda-ba621f77debb · outbound

This paper cites Raissi, P.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Raissi, P

Reference 25

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.692781Z

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Observation 93e74a85-189e-445b-872e-e49f15fd6892 · outbound

This paper cites doi: 10.1007/s10404-026-02899-8.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows doi: 10.1007/s10404-026-02899-8

Reference 26

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.645212Z

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Observation 2acc4191-3516-4945-9a90-e2f406e397c0 · outbound

This paper cites Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Reference 27

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.726583Z

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Observation d3dae6c6-18ed-4d91-8bf1-92c9def9815e · outbound

This paper cites Peyvan, V.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Peyvan, V

Reference 28

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Observation 0fd35b90-a661-4508-94ea-4607a9d9e224 · outbound

This paper cites SVD perspectives for augmenting DeepONet flexibility and interpretability.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows SVD perspectives for augmenting DeepONet flexibility and interpretability

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:57:52.767766Z

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Observation 551be93c-9846-4d92-b7db-d5a0834a8a7b · outbound

This paper cites and Kissas, Georgios and Perdikaris, Paris and Pappas, George J.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows and Kissas, Georgios and Perdikaris, Paris and Pappas, George J

Reference 30

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Observation 352d678e-3255-409d-bbf4-864aff387a51 · outbound

This paper cites E., & Tortorelli, D.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows E., & Tortorelli, D

Reference 31

Resolution: malformed identifier; doi_truncated, observed 2026-05-14T19:57:52.801003Z

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Observation 75022971-ebad-4e01-bf33-7fbb65aae682 · outbound

This paper cites and Balajewicz, Maciej.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows and Balajewicz, Maciej

Reference 32

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.637260Z

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Observation 4aa7fdac-05f6-459d-a079-88ee494a3055 · outbound

This paper cites doi: 10.1137/17M1140571.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows doi: 10.1137/17M1140571

Reference 33

Resolution: verified exact; doi, observed 2026-05-14T19:57:52.805345Z

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Observation 2d40ed94-bfb2-4b77-9116-5f548f015c6d · outbound

This paper cites Discontinuity-aware KAN-based physics-informed neural networks.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows Discontinuity-aware KAN-based physics-informed neural networks

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-08-04T02:29:39.829520Z

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Observation 9876184f-765c-4bff-8a33-d0e7f9ae17b1 · outbound

This paper cites AMR-Transformer: Enabling Efficient Long-range Interaction for Complex Neural Fluid Simulation.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows AMR-Transformer: Enabling Efficient Long-range Interaction for Complex Neural Fluid Simulation

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:57:52.811425Z

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Observation 609a0d98-49f8-4aa9-b59f-28d935735cc1 · outbound

This paper cites $\phi-$DeepONet: A Discontinuity Capturing Neural Operator.

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows $\phi-$DeepONet: A Discontinuity Capturing Neural Operator

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-05-14T19:57:52.708501Z

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Pith citing papers

Observation 22469379-7132-4220-a1ab-13675de36e10 · inbound

Prescribed Wall-Heat-Flux Control of Blockage and Impulse in a Rarefied Micro-Nozzle cites this paper.

Prescribed Wall-Heat-Flux Control of Blockage and Impulse in a Rarefied Micro-Nozzle Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows

Reference 19

Resolution: metadata mismatch; local_arxiv, observed 2026-05-20T03:07:59.735663Z

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Observation 24761d81-4cf1-41da-bdee-04da6ee53e07 · inbound

Gaussian kinetic representations of rarefied nonequilibrium flows cites this paper.

Gaussian kinetic representations of rarefied nonequilibrium flows Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows

Reference 41

Resolution: verified exact; local_arxiv, observed 2026-07-11T02:37:46.720961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.