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Paper Citation Record · LEDGER

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles

As of 16 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:1908.04945.

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

pith.paper-citation-record.v1
1908.04945 v3

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:34:36.971424Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

31 of 31 outbound references displayed

  • verified exact0
  • verified fuzzy14
  • unresolved17
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation bb94e50a-4fce-496c-a9bd-ad67b264f8ba · outbound

This paper cites Scuola Normale Superiore di Pisa (Nuova Serie) [L ecture Notes.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Scuola Normale Superiore di Pisa (Nuova Serie) [L ecture Notes

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.529363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.825843Z digest=sha256:5f15a63f51e3aad48497d37caf3f2093293e266b14c10e9ff326c3a08739747f

Observation 16bd8058-3b55-45c9-8bf9-4f1595acedda · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.510745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.830978Z digest=sha256:651d791fd3d724000568744c6507ffa12bb9c565b4269645585cab0e7a82d17e

Observation 51303b79-89ba-479a-88f6-a528cd8bdd06 · outbound

This paper cites Ra- tion.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Ra- tion

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.496316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.835518Z digest=sha256:57e707ca30045b7a85226ae9b6982c213a7a4059118890012ba252f2d825293e

Observation 6eda6687-cddf-44f2-a772-e526d34e74a7 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.480622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.839418Z digest=sha256:e496e6cb407d2fdbafc296357d2b62d2df0c545675387b8776951375e7dbd42a

Observation cd87934f-b325-4797-b844-fc63d5fb4a48 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.466687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.844215Z digest=sha256:b53e9d355a441b997fe1e3c6cd59db300d6495bdd7d5ab92e2e8b20879eb4d8b

Observation 7c662890-1743-4208-8396-4075d096d9a3 · outbound

This paper cites Differential Equations 229 (2006), no.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Differential Equations 229 (2006), no

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.453017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.848808Z digest=sha256:3fd528affe694e156c4e61221b13f51dc00df4ffe2e979745695bfc0b7ab27e8

Observation 09cb97b0-fd8e-4584-847e-fc25073f193e · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.437254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.853796Z digest=sha256:74573328871ec3ffad93a9ec54c7539d278fbd5b88d44adf4a41f9271b959797

Observation dfcc3375-fcaa-49d0-92be-484d06b8d623 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.422131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.857616Z digest=sha256:9d98be23f7cac57fc530ad5feef95bcb4dcc5ce6ff7a6d5ec75de5180b1dcfb9

Observation a0df04dd-1e7b-4375-9edf-d3a829590d68 · outbound

This paper cites Chen and Hairong Yuan, Local uniqueness of steady spherical transonic shock-fron ts for the three-dimensional full Euler equations , Commun.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Chen and Hairong Yuan, Local uniqueness of steady spherical transonic shock-fron ts for the three-dimensional full Euler equations , Commun

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.410226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.861713Z digest=sha256:7f9d85675b09cfe52f623542ff0869377ab93c496d1ecc46b0b4c0628301c226

Observation 0b01063c-4d29-495a-bc01-044d7a3bb256 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.395878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.865660Z digest=sha256:9dc4ef5932175018377759f20d6e4be284a25dac5158301f411d524d069a4177

Observation e43a58fe-2fff-4cfc-90b0-ac26d8cee0e3 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.380787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.869988Z digest=sha256:d1992fa243d42fcb46fa64fe1959e7e9991fe599876c92563622482b96fea6f3

Observation caa85448-1de2-4b85-9fd4-355ddd722b07 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.361691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.876137Z digest=sha256:d2e50e0fa80771ca4033dea2fd9aa4013e016ee070e72fbabff8db3a4a3b07bc

Observation 46ed12b5-d9b3-4eb6-8fa1-e0eaa7b893d6 · outbound

This paper cites Courant and K.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Courant and K

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.346175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.881890Z digest=sha256:8ef86aa1f340271176f9f25cc4ee75a517f9ed853ca31d37243e70a5264491ac

Observation 94219efc-0db3-46ba-96e2-903bb0335a12 · outbound

This paper cites 105, Princeton University Press , Princeton, NJ, 1983.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles 105, Princeton University Press , Princeton, NJ, 1983

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.328766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.887774Z digest=sha256:e3cbc52931de4e988cdc5d132ac495f951c85e18c9275121593e09fa3f14d0c0

Observation 310175d8-6104-44f8-82c7-234591590aaf · outbound

This paper cites Scuola Normale Superiore di Pisa (Nuo va Serie) [Lecture Notes.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Scuola Normale Superiore di Pisa (Nuo va Serie) [Lecture Notes

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.313713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.892419Z digest=sha256:165a7c870b3d2197f42c82864e50b694a7af1a8ae0e5fdeba39f3f74a641d9be

Observation 47c8fdfb-9c0e-487f-9883-f7b8bb167f4a · outbound

This paper cites 1, Courant Institute of Mathematical Sci ences, New York; American Mathematical Society, Providence, RI, 2011.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles 1, Courant Institute of Mathematical Sci ences, New York; American Mathematical Society, Providence, RI, 2011

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.293676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.897128Z digest=sha256:377a2edf2d271f41dffdeccb4aee7936fb265f43d773d1e0397c6603fabdd9d2

Observation 4abb5233-a300-4181-969d-07df8290e361 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.279672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.903116Z digest=sha256:1b7dbe553835c2901650d219fbafb1f8ece5716ce5ecd30a86a3c0f66af71310

Observation 15eff032-dd06-4824-af0c-87fd8c0cd777 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.261411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.908396Z digest=sha256:f543a1e5c1a1c67f954557aeafaebb09a430ae5ecbc57ab375551b2ad1fd8503

Observation 2f05436a-9ad5-47ee-8f4b-532936edd1a5 · outbound

This paper cites Differential Equations 248 (2010), no.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Differential Equations 248 (2010), no

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.241224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.912762Z digest=sha256:930860192d8ab7928964fca829abc1c2d0ad8851f3386cd7431a53f69be50b3d

Observation 4cf4ee5d-009c-4db9-9b87-fbff79518792 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.228505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.917188Z digest=sha256:08b002ede9b8c339b58a6b386be9893499d160a9568ce44ba1ae8c5a2da029d4

Observation 1016c4cf-884e-4b18-af68-c01259c03254 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.214728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.921978Z digest=sha256:beac7e30d575a52381a9f7cba1990b0ca9edaa6f6a63b36ce2cf3e00b6dafea8

Observation 42aed2fe-31c0-4164-8cf2-ed18d1d357ea · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.200620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.926115Z digest=sha256:e35cd63d68dd1fdc223e197165a1d487a920c9852a4012f2766ef0af8c4ce6c5

Observation ba97ce78-c072-4376-aa83-3ffde258cc0c · outbound

This paper cites Hyperbolic Differ.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Hyperbolic Differ

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.181879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.930637Z digest=sha256:9e1a87b9d87a4b09ed11cf91a377bbc5805fa39600fd104c726aea77ef4b7714

Observation 2c98375a-0d90-4788-b8f6-76b8d17ba8be · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.166508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.935499Z digest=sha256:b7ae5d69c6e1d8bef7f347ef7b6154aeb88c8649006938580af28696bb61151d

Observation fdd25bd8-d77b-448e-9dcb-e7fcc6b068e3 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.148471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.941085Z digest=sha256:e6648be80e30ae0470404e001f3b3f905581c521e6b614cb73f413c62a639929

Observation 089b33ed-7d73-44da-906e-b026c67e2f9f · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.122941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.946375Z digest=sha256:239f77947948be6e5a5d31e407e0bdc3ede508b8223298044c60645ad96091b6

Observation 8043de63-18ab-42d2-8467-8a6c69a844dc · outbound

This paper cites Differential Equations 245 (2008), no.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Differential Equations 245 (2008), no

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.103184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.951530Z digest=sha256:94eacf6768b227b2dc8ae8ec7549ae6f3c432e2ef0b1a12bbe51b9efadc920f7

Observation 48b6a420-6bbf-4d57-b7c2-bcd28323b318 · outbound

This paper cites an unresolved cited work.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:34:37.086247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.957677Z digest=sha256:1e14e26ffdc0d8517aaa44e306113ee4d4f9bffcce70bcff9d44bd084fd62c59

Observation ba65b59e-4ef8-414e-81c9-038c7b6be562 · outbound

This paper cites 66 (2007), no.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles 66 (2007), no

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.066351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.963171Z digest=sha256:36d3b3133f8d0c794eb02f74aa31f1d26e68049c1a613523e17d1fa96758a086

Observation 0a72b57a-d02b-403d-a6cb-9ee87ad3b4cb · outbound

This paper cites Real World Appl.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Real World Appl

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.047582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.967427Z digest=sha256:7a881e7be990c6eadea97080676f4b109ddeea9fa3283990e48964b018366a47

Observation 0c535b74-e6c2-4354-ab6e-1e133be7e066 · outbound

This paper cites Yong P ark, Department of Mathematics, POSTECH, San 31, Hyojadong, Namgu, Pohang, Gyung- buk, Republic of Korea 37673 Email address : pipablue@postech.ac.kr.

3-D axisymmetric transonic shock solutions of the full Euler system in divergent nozzles Yong P ark, Department of Mathematics, POSTECH, San 31, Hyojadong, Namgu, Pohang, Gyung- buk, Republic of Korea 37673 Email address : pipablue@postech.ac.kr

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:34:37.013194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:34:36.971424Z digest=sha256:820b2fe6f9549e5f6cd0923a940071cd6a2710eee2af452832fb8d6761c1978e

Pith citing papers

No inbound Pith citation observations are available.