Paper Citation Record · LEDGER

Dynamics of Bubbling Wave Maps with Prescribed Radiation

As of 22 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:1908.08512.

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

pith.paper-citation-record.v1
1908.08512 v1

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:46:13.371209Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

45 of 45 outbound references displayed

verified exact0
verified fuzzy33
unresolved12
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 094bf05b-c985-49a3-b039-be765f9c7ea1 · outbound

This paper cites Hyperboloidal similarity coor- dinates and a globally stable blowup proﬁle for supercritic al wave maps.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Hyperboloidal similarity coor- dinates and a globally stable blowup proﬁle for supercritic al wave maps

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:14.012756Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e018a228-a375-47cc-8420-f7f30159bf96 · outbound

This paper cites Bourgain and W.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Bourgain and W

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:14.000609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9055b6b5-2570-45aa-9aae-247694fbd77c · outbound

This paper cites an unresolved cited work.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:46:13.989240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a1170f44-177d-46cd-9c45-6dc19995466a · outbound

This paper cites Characterization of large energy solutions of the equivariant wave map problem: I.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Characterization of large energy solutions of the equivariant wave map problem: I

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.976369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 52e60d49-647d-41e8-8189-ce02200281ec · outbound

This paper cites Universality of blow up proﬁle for small blow up solutions to the energy critical wave map eq uation.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Universality of blow up proﬁle for small blow up solutions to the energy critical wave map eq uation

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.964665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e17d2242-bc42-46c3-bfde-b311e9f994d9 · outbound

This paper cites Optimal polynomial blow up r ange for critical wave maps.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Optimal polynomial blow up r ange for critical wave maps

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.952835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8622fe17-2bdc-4b66-a9da-fb59137e0337 · outbound

This paper cites Grillakis.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Grillakis

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.940392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a0a5d2b5-e6ef-47d9-b752-2ad88facb469 · outbound

This paper cites an unresolved cited work.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:46:13.928038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1f10c97e-ff17-4963-9f18-9293a8c04098 · outbound

This paper cites an unresolved cited work.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:46:13.913480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6d9fcab0-d41c-48be-816f-252f6e912f37 · outbound

This paper cites an unresolved cited work.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:46:13.900291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c7738346-af89-418e-81df-1d63037f5a60 · outbound

This paper cites Dynamics of strongly interacting unsta ble two-solitons for generalized korteweg-de vries equations.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Dynamics of strongly interacting unsta ble two-solitons for generalized korteweg-de vries equations

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.884620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1dbb4efd-3599-42ca-9d68-d5de6944a262 · outbound

This paper cites Construction of two-bubble solutions for energy-critical wave equations.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Construction of two-bubble solutions for energy-critical wave equations

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.869182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f8028775-d755-49f0-8fc3-0719b3712265 · outbound

This paper cites Two-bubble dynamics f or threshold solutions to the wave maps equation.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Two-bubble dynamics f or threshold solutions to the wave maps equation

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.855139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1e7e4d6b-0706-437c-8556-c7ccb933094a · outbound

This paper cites Asymptotic decomposition for semilinear wave and equivariant wave map equations.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Asymptotic decomposition for semilinear wave and equivariant wave map equations

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.841261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 502b809c-bae4-4fbb-9ccb-4a93fd04abaa · outbound

This paper cites Krieger, W.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Krieger, W

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.826820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c80e5c96-bb78-4911-84cd-673e73a6bd9d · outbound

This paper cites On stability of blow up solutions for the critical co- rotational wave maps problem.

Dynamics of Bubbling Wave Maps with Prescribed Radiation On stability of blow up solutions for the critical co- rotational wave maps problem

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.808232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cee5a5f0-e2aa-4b7e-8103-8082986dbe30 · outbound

This paper cites Manton and P.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Manton and P

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-14T11:46:13.246465Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 96e78e89-3ecc-49ef-a01d-a030d034830b · outbound

This paper cites an unresolved cited work.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:46:13.785442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5c600981-1ab2-4a21-b9b9-0b5eb8f80520 · outbound

This paper cites Martel, F.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Martel, F

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.772568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b0f7cfe9-7f0c-483a-adaa-0a52c6420fcb · outbound

This paper cites Martel, F.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Martel, F

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.759149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 629c978f-095c-4900-b183-370c53d9c9ad · outbound

This paper cites Martel, F.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Martel, F

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.745918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dab7c563-076e-4dbe-9944-90410def07a3 · outbound

This paper cites Blow up and near soliton dynamics for the L2 critical gKdV equation.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Blow up and near soliton dynamics for the L2 critical gKdV equation

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.732745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a2ed8624-56e2-4cdc-9176-6503adb48914 · outbound

This paper cites an unresolved cited work.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:46:13.718478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f336b449-c0b7-44c5-bbd6-09204a717f82 · outbound

This paper cites Blow up for the critical generalized Korteweg– de Vries equation.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Blow up for the critical generalized Korteweg– de Vries equation

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.705627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ceee7f49-e6b1-4bd7-96a9-fa875fa0ef11 · outbound

This paper cites Blow up for the critical gKdV equation.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Blow up for the critical gKdV equation

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.691479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 56062c91-c668-41ff-b688-6690f781cd75 · outbound

This paper cites Blow up for the critical gKdV equation III: exotic regimes.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Blow up for the critical gKdV equation III: exotic regimes

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.676789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5eaacbc9-3805-4721-ba56-a31fa9154d68 · outbound

This paper cites an unresolved cited work.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:46:13.663577Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4bbe6042-d55c-444f-aa8a-5ef087342506 · outbound

This paper cites an unresolved cited work.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-14T11:46:13.290764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ed97a5c-449a-4762-93da-d12157399a00 · outbound

This paper cites Merle and P.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Merle and P

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.640026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 42abe450-9791-4110-b18e-5231644d6136 · outbound

This paper cites Merle and P.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Merle and P

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.626772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 05c94171-c11b-47ab-b005-616ce88776ce · outbound

This paper cites Merle, P.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Merle, P

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.613248Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 01a8a28b-ecf2-4064-803d-2dba652f00a9 · outbound

This paper cites On universality of blow -up proﬁle for L2 critical nonlinear Schr¨ odinger equation.Invent.

Dynamics of Bubbling Wave Maps with Prescribed Radiation On universality of blow -up proﬁle for L2 critical nonlinear Schr¨ odinger equation.Invent

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.598937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5498c318-9f26-49f8-bb28-212575a09e24 · outbound

This paper cites The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schr¨ odinger equation.Ann.

Dynamics of Bubbling Wave Maps with Prescribed Radiation The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schr¨ odinger equation.Ann

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.585122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d1cda535-210f-4c07-94a6-605dfd911938 · outbound

This paper cites Proﬁles and quantizati on of the blow up mass for critical nonlinear Schr¨ odinger equation.Comm.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Proﬁles and quantizati on of the blow up mass for critical nonlinear Schr¨ odinger equation.Comm

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.570488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 12025a94-2514-42a1-9769-03bfebd619b9 · outbound

This paper cites On a sharp lower bound on the blow-up rate for the L2 critical nonlinear Schr¨ odinger equation.J.

Dynamics of Bubbling Wave Maps with Prescribed Radiation On a sharp lower bound on the blow-up rate for the L2 critical nonlinear Schr¨ odinger equation.J

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.555602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3a429d97-dd97-4e68-b067-2ce93dc3de48 · outbound

This paper cites Rapha¨ el and I.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Rapha¨ el and I

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.540995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2f18e794-9aa9-40aa-affc-d8f65329b0ac · outbound

This paper cites Rapha¨ el and J.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Rapha¨ el and J

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.527626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation df73d9dc-1796-4e47-b122-ee852fc04086 · outbound

This paper cites Rodnianski and J.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Rodnianski and J

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.512921Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2add3d54-9be2-4300-8959-891f4399e97c · outbound

This paper cites Threshold dynamics for corotational wave maps.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Threshold dynamics for corotational wave maps

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.498160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0757b0ce-1101-4638-97aa-537d09105406 · outbound

This paper cites Shatah and M.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Shatah and M

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-14T11:46:13.348073Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6fc42649-63fb-4f04-b583-6c2bbba1a7f0 · outbound

This paper cites Shatah and A.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Shatah and A

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.468908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6e90f623-0cfb-4875-86d7-36767665f914 · outbound

This paper cites an unresolved cited work.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:46:13.454957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dc01b435-cd39-493a-b43b-9e5037257a9e · outbound

This paper cites Uniqueness for critical nonlinear wav e equations and wave maps via the energy inequality.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Uniqueness for critical nonlinear wav e equations and wave maps via the energy inequality

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.440172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5256b8a8-ca57-4e5c-a27d-a76a24104586 · outbound

This paper cites Reverse bubbling and nonuniqueness in t he harmonic map ﬂow.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Reverse bubbling and nonuniqueness in t he harmonic map ﬂow

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T11:46:13.425358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e530545a-727d-49d1-a8e7-4a0b9f81362f · outbound

This paper cites an unresolved cited work.

Dynamics of Bubbling Wave Maps with Prescribed Radiation Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-14T11:46:13.409482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.