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Paper Citation Record · LEDGER

Long-time asymptotics of the defocusing mKdV equation with step initial data

As of 9 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2506.01570.

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

pith.paper-citation-record.v1
2506.01570 v2

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:58:39.377696Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

38 of 38 outbound references displayed

  • verified exact0
  • verified fuzzy24
  • unresolved14
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 124becc7-ca9f-4b04-a81d-89aa17a9d3bc · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:48.948799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:34.828338Z digest=sha256:3bf01fde24c4a37573b7a3a8483dcf2de65f577e14929da70d9dc0e401604c75

Observation da90f0e1-f7ed-4a42-8649-b078dbe74755 · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:48.665212Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:34.905019Z digest=sha256:7ca70424d63f14be94f5a67aaab30b672c8ca8cdb66ae5449aa34734d72a2d61

Observation ccdbdee8-565b-46ff-b72c-a96f9a10691b · outbound

This paper cites Andreiev, I.

Long-time asymptotics of the defocusing mKdV equation with step initial data Andreiev, I

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:48.434239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:35.040194Z digest=sha256:a8b20ffd9861e42ce7b704bfbab00adee5741fe136db3ba152abb453f36c9a80

Observation f743d789-3e48-40fc-9cfd-e6eed37707fe · outbound

This paper cites Beals, R.

Long-time asymptotics of the defocusing mKdV equation with step initial data Beals, R

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:48.207391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:35.198159Z digest=sha256:2439e4e0c9f5f73dd39dd866662dbf50d69d93324c72a8c26e4f638dba888513

Observation 514d81f6-3a9a-417f-8947-90843c284390 · outbound

This paper cites Bertola, A.

Long-time asymptotics of the defocusing mKdV equation with step initial data Bertola, A

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:47.985052Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:35.295985Z digest=sha256:b6c32b65b9c6e49db7f4874989e0f39d2915d15d0f1a132ba294c1e11760fddd

Observation 72ac3ff2-42e0-4d20-8061-292ac49fe87f · outbound

This paper cites Biondini, S.

Long-time asymptotics of the defocusing mKdV equation with step initial data Biondini, S

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:47.747950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:35.435704Z digest=sha256:0897a8e383c5d3ac30bd586d1583eb95e4e65cdfa25b84d8ec61692cd1d2d9ed

Observation 602e420d-5125-4f4c-940d-3b23d091292d · outbound

This paper cites Boutet de Monvel, A.

Long-time asymptotics of the defocusing mKdV equation with step initial data Boutet de Monvel, A

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:47.513306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:35.569473Z digest=sha256:24b056840353424c506b739729b820ca38e55d73bec892ac51960d32ed7c0a3a

Observation c633acaf-9342-4c4a-9ab1-e7fefd9d7ce2 · outbound

This paper cites Boutet de Monvel, V.

Long-time asymptotics of the defocusing mKdV equation with step initial data Boutet de Monvel, V

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:47.256900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:35.699654Z digest=sha256:22d3aeb9e886604bf2bd7e6f182dfde48e7b0fa54a24821a371da78ee3e359b1

Observation 7bb1f0c6-5adf-46ad-b26a-f0324782280e · outbound

This paper cites Boutet de Monvel, J.

Long-time asymptotics of the defocusing mKdV equation with step initial data Boutet de Monvel, J

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:47.007004Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:35.898082Z digest=sha256:d8f6a472b5db979b5ffbf951a63e0386df6d461a6b1c2ad4144ef66362063a1b

Observation 097bd611-f865-4d3e-948d-59c4a583bea1 · outbound

This paper cites Buckingham, S.

Long-time asymptotics of the defocusing mKdV equation with step initial data Buckingham, S

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:46.789891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:36.012365Z digest=sha256:0d5ff7874f418c6b27bd32f3333485d26dadd021f7ca7a42b09177427a0b9a14

Observation 13fde12c-c973-4eef-a5f7-b7fbe3b03344 · outbound

This paper cites Cuccagna and R.

Long-time asymptotics of the defocusing mKdV equation with step initial data Cuccagna and R

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:46.543036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:36.095806Z digest=sha256:e7ebc72421c4f792d79289630bfeb37e60d48f5f19abe4971782c484ed48f59e

Observation 6327ea1a-2e2c-41b7-bdc9-08f9b9c57fe7 · outbound

This paper cites Deift, X.

Long-time asymptotics of the defocusing mKdV equation with step initial data Deift, X

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:46.248403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:36.222584Z digest=sha256:89b7523131f19d93977630a43985f33bafeca604683b5ffc80f85428eb219e4b

Observation d216a135-4c0d-414b-90fd-7669d4a0eb32 · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:45.929357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:36.333565Z digest=sha256:f2a693e139d67475948c058357f7e44a826ea5fcf724a36fbddd972dcdee14cd

Observation 8992aeb4-b108-4f98-ab6a-7eab59496752 · outbound

This paper cites Egorova, Z.

Long-time asymptotics of the defocusing mKdV equation with step initial data Egorova, Z

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:45.638652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:36.430790Z digest=sha256:c95f8352a7b855248c679b9ae087bb88e933bf8aa51708b5819db83d26c0cf44

Observation 00f2b30a-ddb1-47cb-b182-7644df488f25 · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:45.383149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:36.542165Z digest=sha256:262466a53597aaf3109faf5250f11f3f77e27e8ba341db3815bd42bd7a9398a2

Observation f91845a7-a573-412f-a259-fd415547ea46 · outbound

This paper cites Fromm, J.

Long-time asymptotics of the defocusing mKdV equation with step initial data Fromm, J

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:45.099632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:36.659979Z digest=sha256:f6cc43aa90a3a764a809e602f956f966407d0749697c74def9f628c7ad16905f

Observation d2049487-ea63-4693-a06e-d550e768129f · outbound

This paper cites Grava, A.

Long-time asymptotics of the defocusing mKdV equation with step initial data Grava, A

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:44.854629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:36.825561Z digest=sha256:230e6175f15ad2172afa13bec29a894642bcac3e549d2856f9feead2c542c267

Observation 45b4cd56-e824-4e67-b2c9-ea5b4e1dcd2a · outbound

This paper cites Grava, F.

Long-time asymptotics of the defocusing mKdV equation with step initial data Grava, F

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:44.568622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:36.964960Z digest=sha256:3e4f2db9f09f0bcb5620f34278bd8893fe5d7886e9af5ff84734480246842dd8

Observation b0fff03d-03ef-4c4f-80ca-e6077705df21 · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:44.288183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:37.079532Z digest=sha256:138bc26a5d682d414c4be3892f0a1b3069eba182e60d4fd03c91107eee49fb24

Observation 46c70ed5-c50e-4120-88c5-229ec2e66739 · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:43.964023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:37.208893Z digest=sha256:66827e402733fa6789d5fed7f863863ab98fac51cb60016276f6b916f7cd9738

Observation 97ed7c69-c2de-42cf-99a4-20d63498c660 · outbound

This paper cites Jenkins, Regularization of a sharp shock by the defocusing nonlinear Schr¨ odinger equation, Non- linearity 28 (7) (2015) 2131.

Long-time asymptotics of the defocusing mKdV equation with step initial data Jenkins, Regularization of a sharp shock by the defocusing nonlinear Schr¨ odinger equation, Non- linearity 28 (7) (2015) 2131

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:43.659940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:37.350601Z digest=sha256:6fe9f5eb83adffaa9093ef0914f36cd59ec2de89fdef730869b6bca8d7939450

Observation e2a094f8-d2cc-4652-b518-3d0d2af224e0 · outbound

This paper cites Kakutani, N.

Long-time asymptotics of the defocusing mKdV equation with step initial data Kakutani, N

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:43.392103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:37.485881Z digest=sha256:2036679319a66498fdd0583eb1394fca5c2c736eb0cb18d6e715a12f661b9db7

Observation 5c93343e-9e6c-4608-9524-b9aeeebd6c9f · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:43.065734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:37.573645Z digest=sha256:92d8d211fbd98d1688d7e0f9e1395f4b1dc246d532398690a52abfbb64267a61

Observation 8ddf0f00-0689-40f0-8630-6dd2124e198e · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:42.811504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:37.678047Z digest=sha256:e931d5ecec09c3c454e327293bc3867e0a4dafc4f7a968449c8e765c85db750f

Observation 71ccbc3c-d398-4178-9061-dae22b76dbde · outbound

This paper cites Kotlyarov, A.

Long-time asymptotics of the defocusing mKdV equation with step initial data Kotlyarov, A

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:42.527550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:37.803527Z digest=sha256:db3a07a80f0fe87f8336ee29c345627b8080b14dcd0e366bfa052ed0e83ebba2

Observation 74930868-1f43-4027-8fa9-0e5c8ab5591f · outbound

This paper cites Kotlyarov, A.

Long-time asymptotics of the defocusing mKdV equation with step initial data Kotlyarov, A

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:42.300026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:37.900508Z digest=sha256:22e87f1f69b8dc00d203e6443e72ed0bfefae8141ef446e22ceb2b2a2d372918

Observation d49f4f98-08a6-499e-8e4f-7ca479bcc018 · outbound

This paper cites Kotlyarov, A.

Long-time asymptotics of the defocusing mKdV equation with step initial data Kotlyarov, A

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:42.001000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:37.970240Z digest=sha256:ee353258a500e9b318003ed174cd9a02c98446ab115dad5d008ff77a63626c4a

Observation 46bad7d1-1a67-4b58-96f7-21fdb6c59c98 · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:41.741902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:38.152129Z digest=sha256:0d08369e6d1a6bb18f5ddb9769093ee10616216b63dbb440468843568d9bd383

Observation 398b9fff-a204-4aaf-bba7-64aab611287b · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:41.459848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:38.269793Z digest=sha256:719ed55ebbdb6bc46e5dd7e6ca386bf8657dde5ecd65f70a185e388eae4ae97d

Observation 12b8cd44-ebd3-460e-bf0d-dc94075bac0b · outbound

This paper cites Minakov, Asymptotics of step-like solutions for the Camassa–Holm equation J.

Long-time asymptotics of the defocusing mKdV equation with step initial data Minakov, Asymptotics of step-like solutions for the Camassa–Holm equation J

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:41.200448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:38.402943Z digest=sha256:456c2110b6948cd909915fcca4871f0423f06bd13ba1c0a7acd7d8604514b737

Observation 436f97bd-c66e-4c2f-8d69-541bf6e1c3dd · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:40.964513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:38.536678Z digest=sha256:3c1367d28211ba2a1f21079cda59500a7365cecf879157e0a8c4e4f44601ec4f

Observation e4745446-45f9-4465-8330-76ccf6b77d1f · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-07T11:58:40.739987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:38.665229Z digest=sha256:4a6d7323cc990ae8a218f1fb5cb94bfe8b5fdd8075a6045d284e67d6b4f7deed

Observation 58d6fbd7-c40a-4afb-acf3-22fcd4c38fb8 · outbound

This paper cites Rybalko, D.

Long-time asymptotics of the defocusing mKdV equation with step initial data Rybalko, D

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:40.518599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:38.778114Z digest=sha256:7665fc0b7c1bc109fb8b25a50824abae78a8387bcb89a00da56edf484a0d0bfb

Observation dd8dcb7c-bf20-4f5f-913a-60ab52dcb418 · outbound

This paper cites Tajiri, K.

Long-time asymptotics of the defocusing mKdV equation with step initial data Tajiri, K

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:40.305082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:38.895560Z digest=sha256:9a068368ccc3a321b4cce46129618eed747e262d5f174e91c185374fad0a9ba6

Observation 7fbcd275-7126-4be4-a96a-fcb1a06919ff · outbound

This paper cites Watanabe, Ion Acoustic Soliton in Plasma with Negative Ion, J.

Long-time asymptotics of the defocusing mKdV equation with step initial data Watanabe, Ion Acoustic Soliton in Plasma with Negative Ion, J

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:40.099140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:39.038058Z digest=sha256:59ea83b4dc0d8449e67e5ab295ed1929f07e31572fbe7787c19e6d075d0f0e5c

Observation 6cef6cc7-cb7b-433b-b681-c856860b630a · outbound

This paper cites On the large-time asymptotics of the defocusing mKdV equation with step-like initial data.

Long-time asymptotics of the defocusing mKdV equation with step initial data On the large-time asymptotics of the defocusing mKdV equation with step-like initial data

Reference 36

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no resolver link, observed 2026-08-07T11:58:39.145142Z

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Observation ac5dff61-25da-4702-a28f-11896d4324bf · outbound

This paper cites an unresolved cited work.

Long-time asymptotics of the defocusing mKdV equation with step initial data Unresolved cited work

Reference 37

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raw_fallback, observed 2026-08-07T11:58:39.857771Z

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source=pdf_text observed=2026-08-07T11:58:39.261399Z digest=sha256:5e5accf4035eb2082f66f24de5037ea1b6aed6ca237cb538f65a04e586e46dbc

Observation 740a49a8-8268-4fa7-8053-bc21933726e3 · outbound

This paper cites Zhou, The Riemann–Hilbert Problem and Inverse Scattering, SIAM J.

Long-time asymptotics of the defocusing mKdV equation with step initial data Zhou, The Riemann–Hilbert Problem and Inverse Scattering, SIAM J

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T11:58:39.602267Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T11:58:39.377696Z digest=sha256:b92bd1320fa2716aefd8531724ec9817d80afe2f535025451ff27cd595300843

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