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Paper Citation Record · LEDGER

Unstable mode around the 3D boundary layer flow

As of 12 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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:27.971319Z digest=sha256:b220a114cf9d9a9d0a02b29496841481309de17269f689003557bf0185e6dd64

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.011750Z digest=sha256:85e225b90b8015e380a0ca459c9872f4376b3f53e90da586fedd2de723266c90

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.072302Z digest=sha256:769d7fe670ba554bac2d2d49cbb5625ce11bca232c2da5619383c4cdacd77280

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.135517Z digest=sha256:171863f0653d6803997cbe447420d12b0472d329b69b45d8351f93e864f09cba

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.198675Z digest=sha256:50aaeaff8e284db2650b8324e067b552a3f9ce0f1c68f186ea75b343063a060d

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.259386Z digest=sha256:a729d60cb428db8d98db12a915d7a6c170085f97e45ea35dcb8888e6a13e6315

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.319606Z digest=sha256:9804f2352374b7153a8ebf293486372390c0dccd74c594f479e81e4bcb2116b1

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.380709Z digest=sha256:e6354a10a5428eb9da402d1379b2d558798c30cd0fee55e09c52636668405ba6

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.462689Z digest=sha256:e04df952c07946aa2b414ed4235aa4474bc36700a95a43be36eb2c05455bf413

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.524323Z digest=sha256:4ad0d1c66abea9127d0bc3ccee64f1736237b2e82726b6896ae605ca6b6d3b05

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.648389Z digest=sha256:73872b6c70de4c01dd4b44d21067824aeb6d9dc84c4f5b2220744cbf0039dd83

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.752800Z digest=sha256:e90019000ad81e5547c926876c3057c621a897750af57a1df5f6e3ebb275fe37

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:28.916412Z digest=sha256:df1ca6c7639e43b8abe86e38d91236d1809c9a43f83768b05d371fa0c81ccbc1

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:29.025844Z digest=sha256:4b3311111f36df48511b62cc91b6fd6abae75e6f4d09aa7882a78a8453a06c57

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:29.153824Z digest=sha256:c3931f781ed4e8210c860d312f424bfb6d81f8254ffe02b0c43707cd28dc12e1

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:29.221743Z digest=sha256:9875537ac463319aa2e902eb93e0cebabf5a571c6f865938a08ca256db93c6f9

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:29.368408Z digest=sha256:2c80e58386e069ad1d2d247be23e34019e304f396a78c29e6e6d7cf675e64a2b

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:29.474855Z digest=sha256:9d5c25494d26383182738854ddd33893391112e80bddd8bb8af2bba730e97f57

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:29.585172Z digest=sha256:63c7206340f3cfcc51420cbac2b604d30e9c1f0971160e971ad8c1fe1ec9adc8

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:29.683772Z digest=sha256:1fe6f8c82e9e50f4f5ccb44357761d22a76348d73bd12f92b0779a07df24f45a

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:29.789542Z digest=sha256:9ebb905c8519815971e20b4b008cd0dd359437bed1a54585996972e69e7b2fd3

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:29.895557Z digest=sha256:81751545c048dc5744eec9b98fead952e70121ede633c73821ef2380c9f87d8f

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.004356Z digest=sha256:70750545d6425f031d4a0e71f360b4717f506ee92328e3748a9a438f9ac3624d

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.118083Z digest=sha256:fb7f9c1603cb7a81d55131ab92831e898764be6f7be4f849081d99b911a37edf

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.223122Z digest=sha256:4378b51fb5f46920aaf39fe2d27f086b65c211cbee7a8a2aade855cd0880457a

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.328046Z digest=sha256:8da12e03f517cea6cf9552e5bbcc9532603d47a8812d070f66d56b35c771ec28

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.411064Z digest=sha256:52176a749fb505ffb8e191944cffc74cb47e7d48e4337b99ebbce856d36b6c69

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.483181Z digest=sha256:0ca24b28e019bd2966dfb9a289ede7af13a6090464aa01025fed96d9daf614e6

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.566840Z digest=sha256:d79cefa4a0d73f6aa32a74de82872314910dc94189049fd70dbd50b6204dd928

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.647317Z digest=sha256:4cd2d21bf670afb49a92bcc0de47ef988087449c6bb1fc455563bd7086a9e8f2

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.721781Z digest=sha256:3ce4a5cf1707b3dc8ded9b946dbc84b3e82eb03368cba5129d2eb9424a84eba3

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.828440Z digest=sha256:3cd73645fa01fe3d9676d677644f8df34a7e31e004f918ec51abedee604d5e3f

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.898325Z digest=sha256:3d10b7f33be29411cf51d5dc445035f27f0c3eb69d78a97fa9b4fde17eb0db2a

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:30.976816Z digest=sha256:5ee2660977a97c2f9f4bb28263e7b547132880bb1004ed1a670de797e2d38b4c

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:31.043197Z digest=sha256:8e545b96072d9ad0aedeecb742dcad09c0a17ec6b3aa68e7c792eb4e201dd541

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T04:44:31.138310Z digest=sha256:09897f600c558ea7c9e9377330e869801a6d8b2583ab730f0ba80d138dc45b1b

Pith citing papers

No inbound Pith citation observations are available.