Paper Citation Record · LEDGER

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D

As of 14 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 1 inbound Pith citation observation for arXiv:2412.21170.

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

pith.paper-citation-record.v1
2412.21170 v1

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:21:37.481479Z

measured 48 of 48 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-23T01:12:37.650233Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-23T01:15:17.204328Z

Reference resolution

47 of 47 outbound references displayed

verified exact24
verified fuzzy4
unresolved19
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 63d9fede-1268-4187-b97a-3d82a63cb222 · outbound

This paper cites Abenda, http://www.numdam.org/item/AIHPA_1998__68_2_229_0 Solitary waves for M axwell-- D irac and C oulomb-- D irac models\/ , Ann.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Abenda, http://www.numdam.org/item/AIHPA_1998__68_2_229_0 Solitary waves for M axwell-- D irac and C oulomb-- D irac models\/ , Ann

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:21:38.416900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0dd68ed3-aaed-49e5-a28d-a47518ef1d6e · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-10T23:21:37.309090Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7e0aa615-71db-4010-b282-78099db2b2f8 · outbound

This paper cites Bialynicki-Birula and Z.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Bialynicki-Birula and Z

Reference 3

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.768827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9a775924-362c-4ef1-bc1e-d1bbf9b1531a · outbound

This paper cites Berkolaiko and A.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Berkolaiko and A

Reference 4

Resolution: verified exact; raw_fallback, observed 2026-08-10T23:21:38.240366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1b138128-624e-445a-87c2-7c7c790a0f82 · outbound

This paper cites Boussa \" d and A.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Boussa \" d and A

Reference 5

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.757305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a6be46fe-1623-4369-a465-4c5b2731fcde · outbound

This paper cites Boussa\" i d and A.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Boussa\" i d and A

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T23:21:37.326273Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d2655056-826f-4712-b809-4616f26775cf · outbound

This paper cites Boussa \" d and A.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Boussa \" d and A

Reference 7

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.739327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 904d4b6d-240c-4e35-985e-eb24ff0bb76c · outbound

This paper cites Boussa \" d and A.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Boussa \" d and A

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-10T23:21:37.334428Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 514763f1-eeb4-45c3-a3d2-76815fb23fa8 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:21:38.403661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4fb23519-8153-4bf7-bc59-eddac40f7473 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T23:21:37.342809Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb13867e-df40-4899-863c-71ebb090a1f0 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T23:21:37.346570Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30cb9453-dc70-4ed9-bf65-df4b5de0c7cd · outbound

This paper cites Bournaveas, http://dx.doi.org/10.1080/03605309608821204 Local existence for the M axwell-- D irac equations in three space dimensions\/ , Comm.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Bournaveas, http://dx.doi.org/10.1080/03605309608821204 Local existence for the M axwell-- D irac equations in three space dimensions\/ , Comm

Reference 12

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.721173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b49435ec-a7af-4d92-a066-bf1b206d9157 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:21:38.392481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6e372ac5-a5a1-467a-bfea-79670422ae0c · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 14

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.710091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation fec2e662-59c5-47a2-8b95-3fc7008b3e5d · outbound

This paper cites Cuevas-Maraver, P.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Cuevas-Maraver, P

Reference 15

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.698573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7cd63093-f1e1-4ebe-9e25-b2fead73d424 · outbound

This paper cites Comech and D.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Comech and D

Reference 16

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.684682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 84a8c1e4-f0b8-4a30-b174-8687240be973 · outbound

This paper cites Comech and M.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Comech and M

Reference 17

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.672714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b9c3fae3-9f51-451f-99d4-ec5fed2d84d5 · outbound

This paper cites Derezinski, Open problems about many-body D irac operators\/ , Bulletin of International Association of Mathematical Physics (2012).

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Derezinski, Open problems about many-body D irac operators\/ , Bulletin of International Association of Mathematical Physics (2012)

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:21:38.380232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 46c470f6-a040-4c75-b76a-d597c52ad74b · outbound

This paper cites Dvali, M.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Dvali, M

Reference 19

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.660870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2f9b7232-da08-4680-9154-5968a7265c30 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-10T23:21:37.379766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7ec58fc-7cb2-4e0d-b264-ec736b50a38e · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 21

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.648723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 49584655-12db-4d9c-bade-9800d1e613a5 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 22

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.637153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 11f6bd01-8734-4bad-8494-73fa0dd83982 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 23

Resolution: verified exact; raw_fallback, observed 2026-08-10T23:21:37.943224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f5667869-9249-4dd2-adb0-b7f47b53d7bf · outbound

This paper cites Everschor-Sitte, J.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Everschor-Sitte, J

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-10T23:21:37.394870Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54a42a6c-ac8c-4d34-9243-3f2e9fbaa5a7 · outbound

This paper cites Franchini, M.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Franchini, M

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-10T23:21:37.398873Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1fadf857-906d-4bee-81a2-cd8f29766118 · outbound

This paper cites Galindo, http://dx.doi.org/10.1007/BF02785129 A remarkable invariance of classical D irac L agrangians\/ , Lett.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Galindo, http://dx.doi.org/10.1007/BF02785129 A remarkable invariance of classical D irac L agrangians\/ , Lett

Reference 26

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.612028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9d93fd71-3b3d-41cf-8dcf-887919eec349 · outbound

This paper cites Gross, http://dx.doi.org/10.1002/cpa.3160190102 The C auchy problem for the coupled M axwell and D irac equations\/ , Comm.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Gross, http://dx.doi.org/10.1002/cpa.3160190102 The C auchy problem for the coupled M axwell and D irac equations\/ , Comm

Reference 27

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.599988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cc7ea8d8-d7ea-4810-b646-a9b4e39b1faa · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:21:38.365898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d7e64e92-a5ce-44e3-9077-4a1aed240611 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 29

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.587875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1087cc30-2e9a-4564-b563-2f1640b874c8 · outbound

This paper cites Kamyshkov, J.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Kamyshkov, J

Reference 30

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.575567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1ce99e7a-0712-4e06-b127-4bb49102c7a6 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 31

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.563206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 971e20b0-0a8d-4fab-996c-c007b75c7e06 · outbound

This paper cites Kalf and O.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Kalf and O

Reference 32

Resolution: verified exact; raw_fallback, observed 2026-08-10T23:21:37.861760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6c3e7580-70cc-44f9-bcd2-b6b28708c27f · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 33

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.550284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 190c6b88-c379-4624-98de-a2e2f0d93153 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:21:38.352001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8987c5f8-301e-4436-9003-4a374f01c055 · outbound

This paper cites Monastyrskij, https://museum.itmo.ru/images/person/16/ignatovsky1.pdf Ignatovsky and the pre-history of the discovery of topological invariants in Q uantum M echanics\/ (1999).

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Monastyrskij, https://museum.itmo.ru/images/person/16/ignatovsky1.pdf Ignatovsky and the pre-history of the discovery of topological invariants in Q uantum M echanics\/ (1999)

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:21:38.341750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 066ad638-3894-46fe-8f9b-1ed5a9a14e41 · outbound

This paper cites Spectral problems about many-body Dirac operators mentioned by Derezi\'{n}ski.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Spectral problems about many-body Dirac operators mentioned by Derezi\'{n}ski

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:21:37.792758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4cde7fc4-3ca7-410f-abfd-af9bdde78389 · outbound

This paper cites Pauli, http://dx.doi.org/10.1007/BF01397326 Zur Q uantenmechanik des magnetischen E lektrons\/ , Z.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Pauli, http://dx.doi.org/10.1007/BF01397326 Zur Q uantenmechanik des magnetischen E lektrons\/ , Z

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-10T23:21:37.444370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e9f25d88-605c-41e8-b16b-dfdcb2454704 · outbound

This paper cites Phillips, W.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Phillips, W

Reference 38

Resolution: verified exact; doi, observed 2026-08-10T23:21:38.329682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5d84dfa3-5390-4678-9eae-28d9d73534fd · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:21:38.316379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7bdc4da3-3852-408f-aa08-d5d91c838cab · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:21:38.302788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8327e979-5094-4ed1-a059-5575337acd8c · outbound

This paper cites Soler, http://dx.doi.org/10.1103/PhysRevD.1.2766 Classical, stable, nonlinear spinor field with positive rest energy\/ , Phys.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Soler, http://dx.doi.org/10.1103/PhysRevD.1.2766 Classical, stable, nonlinear spinor field with positive rest energy\/ , Phys

Reference 41

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.532912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4014abb0-6828-440d-a4bc-e14964759465 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:21:38.289100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 61d9119e-1db4-4d45-9fa1-aaa19394dfc0 · outbound

This paper cites Thaller, The D irac equation\/ , Texts and Monographs in Physics, Springer-Verlag, Berlin, 1992.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Thaller, The D irac equation\/ , Texts and Monographs in Physics, Springer-Verlag, Berlin, 1992

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:21:38.278770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1ba098eb-1746-4543-b626-700813d44214 · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:21:38.266379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8d1a5b8f-47e9-433d-8c1e-3854b058c90f · outbound

This paper cites an unresolved cited work.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:21:38.254668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4834e79a-3cc8-4391-81d5-9bfcc5610103 · outbound

This paper cites Wakano, http://dx.doi.org/10.1143/PTP.35.1117 Intensely localized solutions of the classical D irac-- M axwell field equations\/ , Progr.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Wakano, http://dx.doi.org/10.1143/PTP.35.1117 Intensely localized solutions of the classical D irac-- M axwell field equations\/ , Progr

Reference 46

Resolution: verified exact; doi, observed 2026-08-10T23:21:37.521135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 19b1fa7b-278c-4e4c-b4c9-dbe24e47431a · outbound

This paper cites Zahed and G.

On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D Zahed and G

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-10T23:21:37.481479Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 160af148-fc58-478d-b801-898d17c5b65b · inbound

Decay of solutions of nonlinear Dirac equations cites this paper.

Decay of solutions of nonlinear Dirac equations On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-23T01:15:17.207182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.