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Paper Citation Record · LEDGER

Unstable mode around the 3D boundary layer flow

As of 13 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2509.06089.

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

pith.paper-citation-record.v1
2509.06089 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T04:44:31.138310Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

36 of 36 outbound references displayed

  • verified exact2
  • verified fuzzy26
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4b5f5c61-6112-4dcb-b8f8-957934450032 · outbound

This paper cites Bian and E.

Unstable mode around the 3D boundary layer flow Bian and E

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:37.333701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:27.971319Z digest=sha256:ade91f2c6edc8253a4bea57addaf78027415327a4ade76dda2851b976ba1d82d

Observation 39b0c916-7608-4ee2-b3e0-af3058639629 · outbound

This paper cites Bian and E.

Unstable mode around the 3D boundary layer flow Bian and E

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:37.131598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.011750Z digest=sha256:126e8d69afa06f53df58bf39c8a67aca7cf6fb8221f4826bac82bd6f380ddd9f

Observation 4e45d49f-ed06-40c3-a0ed-31de62786f05 · outbound

This paper cites an unresolved cited work.

Unstable mode around the 3D boundary layer flow Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-05T04:44:36.955363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.072302Z digest=sha256:51c3d2dbca4e2182dd13d2225e892ab7e01062e4b3dde7c81d8e3800f3cc336c

Observation b080d4c7-a6bb-4bcb-82c1-53f2a51d4aa2 · outbound

This paper cites an unresolved cited work.

Unstable mode around the 3D boundary layer flow Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-05T04:44:36.668175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.135517Z digest=sha256:dbbd19e7686ce0edcce079b78b3edc1d6368a463ed9a1cc712383f8b111ad64a

Observation 7a2ebd7f-50d7-4d08-847b-1b06556c7e5f · outbound

This paper cites an unresolved cited work.

Unstable mode around the 3D boundary layer flow Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-05T04:44:36.440332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.198675Z digest=sha256:fd3d2bac4843d2ef5e0d9c9d4db7c2c45ed2e2368798e40289fd80c1d6f343a9

Observation 7be71661-f2d3-493a-879e-27f3a31f0acf · outbound

This paper cites Gallaire, D.

Unstable mode around the 3D boundary layer flow Gallaire, D

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:36.199717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.259386Z digest=sha256:dacf9a1d6cd5efa81ab0fe25f8c9c93b41c2032ab67ebb66da23f514fa1e33a3

Observation 605f6b51-5f44-4037-bd7d-df377ec407d8 · outbound

This paper cites G´ erard-Varet and Y.

Unstable mode around the 3D boundary layer flow G´ erard-Varet and Y

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:35.935740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.319606Z digest=sha256:0b9643ea435811c4deacfe19ac5aee8a7ad17b27eabe95b51c3b0088e7aa1012

Observation 1650ddd9-49a7-4e26-87a5-dcd8a555f0e5 · outbound

This paper cites G´ erard-Varet and E.

Unstable mode around the 3D boundary layer flow G´ erard-Varet and E

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:35.718017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.380709Z digest=sha256:c3d650578077548b54e606d3751fcec38d7a5d727c0eb08616aa8c2d7978a305

Observation 6b121e06-450a-4445-b9ce-286c77af1e58 · outbound

This paper cites G´ erard-Varet, Y.

Unstable mode around the 3D boundary layer flow G´ erard-Varet, Y

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:35.531631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.462689Z digest=sha256:0a0dc7984fadf5a459942e83671354ad39fcdaf2bade8898183ea93009e2a06c

Observation dbc29c5e-ed7e-4adb-8d9d-1b19dbfef06d · outbound

This paper cites G´ erard-Varet, Y.

Unstable mode around the 3D boundary layer flow G´ erard-Varet, Y

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:35.337876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.524323Z digest=sha256:59ee91910bcdf10794f44febeb5d2a0981784b4302b8ba51fd045398b9900358

Observation d3a85ea5-c730-4176-b16c-af7ac6485d45 · outbound

This paper cites Grenier,On the nonlinear instability of Euler and Prandtl equations, Comm.

Unstable mode around the 3D boundary layer flow Grenier,On the nonlinear instability of Euler and Prandtl equations, Comm

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:35.153695Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.648389Z digest=sha256:a3eaba13848fd7b040b89a9adfeda051bce34e5272a1fe3b8381a4a0a976c09f

Observation 83baf38f-0d36-4733-9cfd-3c224bed81fc · outbound

This paper cites Grenier, Y.

Unstable mode around the 3D boundary layer flow Grenier, Y

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:34.972782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.752800Z digest=sha256:cf0199e1b3f61b84a60a87f8b67b897b6daf48c5d042c30efdb3875bb9063902

Observation f84a0554-51b1-467f-9f1a-edb53b9cbdd4 · outbound

This paper cites Grenier and T.

Unstable mode around the 3D boundary layer flow Grenier and T

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:34.776828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:28.916412Z digest=sha256:9f6c2d277a3e6e0a949fbcc8ff567850c63c695b1df1976cc8aaa8c2863534cc

Observation 390f3e39-36a8-448b-99b2-fa3220f0e682 · outbound

This paper cites Grenier and T.

Unstable mode around the 3D boundary layer flow Grenier and T

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:34.602497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:29.025844Z digest=sha256:f4c66aca6ad4f246ac1c24222ce0ffea76964893a170e015db69c8191c0b8bfb

Observation 871a9763-a8e9-41ce-a8e2-79054f739cf7 · outbound

This paper cites Guo and S.

Unstable mode around the 3D boundary layer flow Guo and S

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:34.420406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:29.153824Z digest=sha256:fb5eb0f9b072b62aa370cbc9cb3d41826b518975b670cfa4cfceca66b42ca75b

Observation ee008512-c6bf-4eab-b638-14e311cde986 · outbound

This paper cites Global-in-$x$ Stability of Steady Prandtl Expansions for 2D Navier-Stokes Flows.

Unstable mode around the 3D boundary layer flow Global-in-$x$ Stability of Steady Prandtl Expansions for 2D Navier-Stokes Flows

Reference 16

Resolution
verified exact
local_arxiv, observed 2026-08-05T04:44:31.484168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:29.221743Z digest=sha256:695c762553bb3b3f9fede6a166ba09fef4177abc6342a78e6529855bbfa6f479

Observation 2353d1b6-c39a-41e9-aa13-9c0c3f60e171 · outbound

This paper cites Kukavica, V.

Unstable mode around the 3D boundary layer flow Kukavica, V

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:34.288222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:29.368408Z digest=sha256:af796da85c8166b10890f978353c788eb7e2830d4ead0c9b2a3c59f892fb3cb1

Observation 3dbfbbf3-e91f-4bad-b0f8-f69b80ad7ecb · outbound

This paper cites Li, N, Masmoudi and T.

Unstable mode around the 3D boundary layer flow Li, N, Masmoudi and T

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:34.146297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:29.474855Z digest=sha256:45b21c22a7332b0cab8c0e9e310e97022eb0b5d3e58dfe67016c4849f123a283

Observation 73b54a34-8528-47e0-a739-21cb3824783b · outbound

This paper cites Liu , Y.-G.

Unstable mode around the 3D boundary layer flow Liu , Y.-G

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:33.967555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:29.585172Z digest=sha256:d1651148b862f20769f7d7dbcd3545bdec28880a2fda19053a9ccedbfd35701f

Observation c83f0c27-f712-414f-85da-1c56f8e765c1 · outbound

This paper cites Liu , Y.-G.

Unstable mode around the 3D boundary layer flow Liu , Y.-G

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:33.856467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:29.683772Z digest=sha256:c4f95d63920a0df98978f338828be57f927c89b63fcb5647a4c99bea8d2e4ae7

Observation fff1b9ad-3987-4e34-a768-59c5b7bcce71 · outbound

This paper cites Liu , Y.-G.

Unstable mode around the 3D boundary layer flow Liu , Y.-G

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:33.716796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:29.789542Z digest=sha256:24c7e110e2d02e7df623b96e5c16b6c053b48c455996d283c25d233968917e87

Observation e091ece5-3789-4b2d-8052-b315cd749745 · outbound

This paper cites Maekawa,On the inviscid limit problem of the vorticity equations for viscous incompressible flows in the half-plane, Comm.

Unstable mode around the 3D boundary layer flow Maekawa,On the inviscid limit problem of the vorticity equations for viscous incompressible flows in the half-plane, Comm

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:33.581345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:29.895557Z digest=sha256:b0222706f13a450e770952d398ead483f92abf4bc29104c29747ff3c580fabe7

Observation 420d6f3d-0448-4e4e-b40f-11365578ff4d · outbound

This paper cites Maekawa and A.

Unstable mode around the 3D boundary layer flow Maekawa and A

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:33.447636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.004356Z digest=sha256:b4e9c3e412016b51acbc54f2c775e5565920c82a59dc24dc823f8e0dd5631bf4

Observation 0ccb5ddf-8e34-4f19-bef5-c9e01e8617fd · outbound

This paper cites Mack modes in supersonic boundary layer.

Unstable mode around the 3D boundary layer flow Mack modes in supersonic boundary layer

Reference 24

Resolution
verified exact
local_arxiv, observed 2026-08-05T04:44:31.331744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.118083Z digest=sha256:5e1a5813709d9a0162743fb4f8bd133c319c14e64f70d26a2d6d6c3ef063a316

Observation 184a7265-fc3d-4542-9d50-4a93f62a938d · outbound

This paper cites Masmoudi, Y.

Unstable mode around the 3D boundary layer flow Masmoudi, Y

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:33.300256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.223122Z digest=sha256:7db5e97b7435e8317190c025636caf574ce6acdd96a6d5069b6652b12d245f9e

Observation fccad64f-4a9c-497e-84d6-b592d7c669fd · outbound

This paper cites Mazzucato and M.

Unstable mode around the 3D boundary layer flow Mazzucato and M

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:33.084451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.328046Z digest=sha256:edf6f73482457342bd172354e9ce0007a762b365d1270049f07ba1b4c6406bc6

Observation fba89a99-bfe3-4568-97f9-acc445466f09 · outbound

This paper cites Nguyen and T.

Unstable mode around the 3D boundary layer flow Nguyen and T

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:32.967642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.411064Z digest=sha256:c13dabb4070d47887380c4328c6c93a25e0f768e829b4f2f7cc78e2375c185d7

Observation 5c920bbc-62f7-4b87-9bf0-d9f227012f54 · outbound

This paper cites Prandtl,Uber Flussigkeitsbewegung bei sehr kleiner Reibung, Verhandl.

Unstable mode around the 3D boundary layer flow Prandtl,Uber Flussigkeitsbewegung bei sehr kleiner Reibung, Verhandl

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:32.780675Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.483181Z digest=sha256:c6cc486d123cd72fe99c25539f4ed6835a7092eadd70fc3764abfdeb008dec8d

Observation a14ed589-cc39-4ed7-b4bd-34616bdb11d4 · outbound

This paper cites an unresolved cited work.

Unstable mode around the 3D boundary layer flow Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-05T04:44:32.659696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.566840Z digest=sha256:35f7d6093b269efe90be3dd53190418bd54a7d0d86d3e300190d1e881f83f550

Observation 3d138054-740a-4a7e-aa88-9a0c0e90ed4a · outbound

This paper cites Sammartino and R.E.

Unstable mode around the 3D boundary layer flow Sammartino and R.E

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:32.556839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.647317Z digest=sha256:6e8cbc2adbfffb3a99b4a1c3791bb196acb21bafb479ec54d90ce52e3eef5c96

Observation 6eb65803-f941-4c85-828d-f1f143d91d38 · outbound

This paper cites an unresolved cited work.

Unstable mode around the 3D boundary layer flow Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-05T04:44:32.443682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.721781Z digest=sha256:75414153502a27abc52b24b1df81e52c240af35ff25c89ebb06b0a019d16e401

Observation e7a33a12-7132-4820-ae63-e2f07e39749f · outbound

This paper cites an unresolved cited work.

Unstable mode around the 3D boundary layer flow Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-05T04:44:32.234442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.828440Z digest=sha256:7a5840496ef8c5879845806b0bdb46240f46670f37b5e951a89520dd3aca9545

Observation 339e5764-d4ec-48af-b55d-109ce778eeca · outbound

This paper cites Schlichting, Boundary layer theory, 4th ed., McGraw-Hill Series in Mechanical Engineering, McGraw- Hill, New York, 1960.

Unstable mode around the 3D boundary layer flow Schlichting, Boundary layer theory, 4th ed., McGraw-Hill Series in Mechanical Engineering, McGraw- Hill, New York, 1960

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:32.116558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.898325Z digest=sha256:a5691ad149fae596eea2289e31af0585a0beeab6d1f17fa94a36e9d9e72dddae

Observation a7140052-d522-4d3f-9edb-84403de19da6 · outbound

This paper cites an unresolved cited work.

Unstable mode around the 3D boundary layer flow Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-08-05T04:44:31.932270Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:30.976816Z digest=sha256:a7ac4f46e37e873bfed1f5f905a44a4e32a6d3a06cf05ee6fd776e3c49c68747

Observation 60b0af38-8ade-4f8b-8efc-eea88a75c34d · outbound

This paper cites an unresolved cited work.

Unstable mode around the 3D boundary layer flow Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-05T04:44:31.769697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:31.043197Z digest=sha256:bd8e8475133c1ee5f0825b46dda89c32ab20e2fb3a72e1466e076051021cc972

Observation ba69a896-e7ac-451c-90c2-33686d045d22 · outbound

This paper cites Yang and Z.

Unstable mode around the 3D boundary layer flow Yang and Z

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T04:44:31.631551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T04:44:31.138310Z digest=sha256:70ee724666d40508dae69c2d077cd0c97f3ec5ebc6fd129234fce2a4e50eeaf1

Pith citing papers

No inbound Pith citation observations are available.