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Paper Citation Record · LEDGER

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations

As of 10 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2506.20775.

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

pith.paper-citation-record.v1
2506.20775 v2

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:49:42.306443Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T22:53:06.136006Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

24 of 24 outbound references displayed

  • verified exact0
  • verified fuzzy18
  • unresolved6
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 44778462-4726-4dfd-af6b-a40562fd9ff9 · outbound

This paper cites Alexandre, J.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Alexandre, J

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.720821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:40.065471Z digest=sha256:71cec0399d86916bf5d61ea98fc419dd0cfda6000375f449a75e4bbd743c1fb5

Observation 835bdf3c-57a7-49d7-ab49-b7a8c6640a22 · outbound

This paper cites Alexandre, Y.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Alexandre, Y

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.701734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:40.149896Z digest=sha256:491c4b9fd762106e0b17bd45c14034884d20406f5c7aa3a07d68285320491863

Observation 390d2bea-edde-49a3-a66d-de4151154965 · outbound

This paper cites Alonso, Y.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Alonso, Y

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.683130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:40.239070Z digest=sha256:ec67bc584808cae1534a6d05ddc7c17713c54300528b077f5fbbc9994fa0d3b2

Observation 39bfe32d-9fa2-4419-bc99-69b6edc85e3d · outbound

This paper cites Anceschi and Y.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Anceschi and Y

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.666151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:40.302710Z digest=sha256:79b9658863e3907209097cc5298443acc203e702d551919f1246afca4a1fee11

Observation cdd45a5d-cd89-468c-a2ac-b0884bebf65c · outbound

This paper cites Desvillettes and C.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Desvillettes and C

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.651117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:40.452475Z digest=sha256:3d06283d79e1d43222e3df7a334eff3d9f3a55662db2eab5e68bf2178ce01f90

Observation 61bcc3b4-1138-41a5-9208-27ddd8bfd7f4 · outbound

This paper cites an unresolved cited work.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:49:42.635211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:40.662604Z digest=sha256:7d39ed267dcdc2083f2bb2495dbe048aa546c9d80df70b363c0eb32fa5c79c45

Observation 283de405-4274-405c-9c8a-119fa754239a · outbound

This paper cites an unresolved cited work.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:49:42.620163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:40.762569Z digest=sha256:4ced428dd4af5fad6c55c9f437dc33213fa72c782940ce745b92cd16366a5c62

Observation be3d872e-ad5b-4cc5-998e-f7473435326f · outbound

This paper cites an unresolved cited work.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:49:42.606258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:40.871075Z digest=sha256:38ed655e9561bcc3c4e472ac29661c34601750096b9f55f5b99e8391e9f582fe

Observation af8476e7-3c0d-4128-94bd-66595c76ee64 · outbound

This paper cites Fournier,Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb poten- tial., Comm.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Fournier,Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb poten- tial., Comm

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.590606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:41.039516Z digest=sha256:2117262de3741cfcd059199ab957b4441c247e2f102bb641e1ee38bef884b1eb

Observation 521763bb-ff52-4d6e-998d-4e63762e702b · outbound

This paper cites Fournier and D.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Fournier and D

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.575646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:41.183706Z digest=sha256:534ca0690fd7a5e75271451f307eccd66a8d6f16b7c92eadf035aa6876ee5e37

Observation ace416f9-5828-4bac-bd62-efc84b8a75e0 · outbound

This paper cites Fournier and H.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Fournier and H

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.561416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:41.345305Z digest=sha256:01e7acb708b0a402dc2acf994d261acfcb0c418cb522240651251ba1f296376e

Observation 0c874d99-ee5f-4474-bd83-aa63ad9fc8b0 · outbound

This paper cites Golding, M.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Golding, M

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.546826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:41.509325Z digest=sha256:0c540648486c0713ed025918c5149d4afd48fd4c98c288b91d1b0c0bea486d80

Observation ac9379e3-e304-47f1-bb17-e63da2a0818c · outbound

This paper cites an unresolved cited work.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:49:42.532713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:41.675789Z digest=sha256:882dbf339a230f10ba7530e3645bfff7d9b5766549d506a10140f973e7bbb088

Observation 358ef052-39e7-466b-bd30-08f1bee2e1e9 · outbound

This paper cites Existence, uniqueness and smoothing estimates for spatially homogeneous Landau-Coulomb equation in $H^{-\f12}$ space with polynomial tail.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Existence, uniqueness and smoothing estimates for spatially homogeneous Landau-Coulomb equation in $H^{-\f12}$ space with polynomial tail

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-06T22:49:41.788705Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:49:41.788705Z digest=sha256:dc6f26a19da7184949073e6a81c1cdec83144aa777e88670785f7dbf8005d14c

Observation d24a5614-a694-4ebd-9797-dc31812376fa · outbound

This paper cites Henderson, S.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Henderson, S

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.517480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:41.950401Z digest=sha256:63869cd5ad7ed73c7b376c1d4e897b88df78e20b7f83b68f8b11ef674f1c1766

Observation ead524bc-920f-4572-94a6-0b9c490db6bd · outbound

This paper cites Henderson, S.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Henderson, S

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.500086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:41.974717Z digest=sha256:801dba5dfd24cae788030968400a9b83059d3766f66d770c64958d95e1dfd832

Observation 6a189b19-5790-4973-a083-193bbbc4945a · outbound

This paper cites Henderson and W.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Henderson and W

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.482491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:42.049764Z digest=sha256:fef6059239eb93bb165d8d4fd26a26b3386f3437e9fadf50ea444662fb584f52

Observation 86aa3c38-9128-4db4-8915-bcb01450bac7 · outbound

This paper cites Kumano-Go,Pseudo-differential operators, The MIT Press, 1982.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Kumano-Go,Pseudo-differential operators, The MIT Press, 1982

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.467599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:42.163395Z digest=sha256:c48ec1a106fcbd641a416686fe6d460e848e856681ebbd82c34640bd82633b2f

Observation 6a67cec8-f098-4d19-980c-d647ceea3a33 · outbound

This paper cites an unresolved cited work.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:49:42.450379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:42.223336Z digest=sha256:12581a5c5446d27aabcb6ba0c122ca37fdc778172fc12cb9181892390007cd52

Observation a9ad701f-11cc-4022-9752-b0fc51c63582 · outbound

This paper cites Morimoto and C.-J.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Morimoto and C.-J

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.432422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:42.277209Z digest=sha256:b0c1025e94fb9e14c010183cdfcaf3991b29a5b7b340178819909651101d36dc

Observation 3fa9713d-8647-4c9b-9c4d-5800834ceddd · outbound

This paper cites Mouhot and C.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Mouhot and C

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.416984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:42.289407Z digest=sha256:d5ee87d47f515a5cdde98fbbcf284e203bf21de9eb31e4509ab09e542c5bbae6

Observation 5e7bd577-1918-4cdd-859a-fd56e17c866b · outbound

This paper cites Ruzhansky and T.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Ruzhansky and T

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.399289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:42.295023Z digest=sha256:25761f6b7df84bcca1c052922991735b3f6fd528ee8c5718d58903f44d200df2

Observation e6665523-f11b-47df-a716-93a5147a9234 · outbound

This paper cites Turunen and G.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Turunen and G

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.383786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:42.300349Z digest=sha256:4d9b958bc853ae711b6fbb8aea098ea9c321ea6d94959c24ebc38cb4d0c45d98

Observation a3bbc5bf-67b4-4a5a-bfb5-045bb12ca01a · outbound

This paper cites Villani,On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations, Arch Rational Mech Anal143(1998), 273–307.

The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations Villani,On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations, Arch Rational Mech Anal143(1998), 273–307

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:49:42.367699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-08-06T22:49:42.306443Z digest=sha256:94a39c2d347fb5663847e7bb2d8f4cec457b91615e36f84060b2d037cccb2922

Pith citing papers

Observation 27268bb1-bd1d-4055-b56d-81670f91257d · inbound

Uniqueness and Zeroth-Order Analysis of Weak Solutions to the Non-cutoff Boltzmann equation cites this paper.

Uniqueness and Zeroth-Order Analysis of Weak Solutions to the Non-cutoff Boltzmann equation The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-02T22:53:06.136006Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-02T22:53:06.136006Z digest=sha256:dabe2569267a62370926c7916491d54a0a2e77c914172c8a07120ca598b739d6