Pith. sign in

Paper Citation Record · LEDGER

On $m$-order logarithmic Schr\"odinger operator

As of 8 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2606.21056.

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

pith.paper-citation-record.v1
2606.21056 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T14:08:09.929477Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

30 of 30 outbound references displayed

  • verified exact6
  • verified fuzzy0
  • unresolved24
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation add53a7c-5f27-4db3-8234-bbd3405cc55e · outbound

This paper cites Logarithmic S chr\"odinger operators.

On $m$-order logarithmic Schr\"odinger operator Logarithmic S chr\"odinger operators

Reference 1

Resolution
verified exact
arxiv_id, observed 2026-07-04T06:49:38.098766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:ee2d040f1eb81bc9ed656258b6f5d3833a6418b8498f969436cce7cbe9a082ea

Observation a84c226d-570b-4d6f-9ec0-740a42cb730f · outbound

This paper cites Extension theorems for logarithmic Schr\"odinger and discrete Laplacian operators.

On $m$-order logarithmic Schr\"odinger operator Extension theorems for logarithmic Schr\"odinger and discrete Laplacian operators

Reference 2

Resolution
verified exact
local_arxiv, observed 2026-07-04T06:49:38.101159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:1fa71eb0fde325259e2c7d9250d8c76c16d6107cf7a0424bab3b6200ae52e9b2

Observation 7233f62c-dc22-4c41-ba71-ad78f7f0aa56 · outbound

This paper cites J., Fari\ na, J.

On $m$-order logarithmic Schr\"odinger operator J., Fari\ na, J

Reference 3

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:fb57537e241ffef5e4f6bc38a6c5f19fb515f36b127c82f3f45837e1e390c09d

Observation f2d5ac99-b3bb-419a-85f6-47b76f098700 · outbound

This paper cites Weighted inequalities for S chr\"odinger type singular integrals.

On $m$-order logarithmic Schr\"odinger operator Weighted inequalities for S chr\"odinger type singular integrals

Reference 4

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:dc2b91e19261c1db4ea8bbe467e6b24a2e14ebdb2a82382201325f3c87ca91f6

Observation 3fe05679-a804-43cf-a2ba-85d6a73cfce7 · outbound

This paper cites On m-order logarithmic Laplacians and related propeties.

On $m$-order logarithmic Schr\"odinger operator On m-order logarithmic Laplacians and related propeties

Reference 5

Resolution
verified exact
arxiv_id, observed 2026-07-04T06:49:38.175595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:0c0d391b3ead538c7c70b80e4b90235c8ff8d844553d021a41e1e5a85a31a47a

Observation 3f5365ee-6fb1-4e05-941a-b726ff74620d · outbound

This paper cites Existence and convergence of least-energy solutions involving the logarithmic S chr\"odinger operator.

On $m$-order logarithmic Schr\"odinger operator Existence and convergence of least-energy solutions involving the logarithmic S chr\"odinger operator

Reference 6

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:189a2aad271cc9003e82783da0cb2abc6ad303f026cda3dd91a9096eeb85ba75

Observation 65fb6d64-94c2-44de-890b-d5c573db38e5 · outbound

This paper cites Bounds for eigenvalues of the D irichlet problem for the logarithmic L aplacian.

On $m$-order logarithmic Schr\"odinger operator Bounds for eigenvalues of the D irichlet problem for the logarithmic L aplacian

Reference 7

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:b9585ba8f5a61ee3ee921223abc0be9ffec63289b4cfe1f722087cbc6e646cd0

Observation 6abacb5f-e310-44d9-a351-5d5c2315aed9 · outbound

This paper cites The C auchy problem associated to the logarithmic L aplacian with an application to the fundamental solution.

On $m$-order logarithmic Schr\"odinger operator The C auchy problem associated to the logarithmic L aplacian with an application to the fundamental solution

Reference 8

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:5019c65f6990d40a2d4c162368a9a2ee32f095e28d6dca4c15b5ac82a6933a53

Observation 1ac72518-e600-4b99-822c-9be4dd62b143 · outbound

This paper cites The D irichlet problem for the logarithmic L aplacian.

On $m$-order logarithmic Schr\"odinger operator The D irichlet problem for the logarithmic L aplacian

Reference 9

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:9ee6eb1c6cf4bbff2a47439d0dc4045eaeb4ac15e780d63a1055414521a7e035

Observation 5d250774-d8b0-46c9-b2fc-69a2e30d9dd3 · outbound

This paper cites Logarithmic Laplacian on General Riemannian Manifolds.

On $m$-order logarithmic Schr\"odinger operator Logarithmic Laplacian on General Riemannian Manifolds

Reference 10

Resolution
verified exact
arxiv_id, observed 2026-07-04T06:49:38.180188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:2f9f2c23b9653a870b177debdc321e91c117b72bbdf24975000097c5ca52ecb0

Observation e37120aa-d90f-4d27-becd-07c5fcd6bc3e · outbound

This paper cites The Logarithmic Laplacian on General Graphs.

On $m$-order logarithmic Schr\"odinger operator The Logarithmic Laplacian on General Graphs

Reference 11

Resolution
verified exact
arxiv_id, observed 2026-07-04T06:49:38.095882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:4f61513882f9ec605f1564aee8fcdba359a8e347d75f61ae506cda9197d95eb6

Observation afc35111-6998-4337-a1c9-b65b6053e7c6 · outbound

This paper cites R., and Fefferman, C.

On $m$-order logarithmic Schr\"odinger operator R., and Fefferman, C

Reference 12

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:6ea8b7f7e7ee6a77895cb0bbaa506c1d4cdc98389fa733267eb58f334349c8e7

Observation 2b2b8b32-52fd-4362-851a-18ccd4a88d06 · outbound

This paper cites Spectral multiplier theorem for H^1 spaces associated with some S chr\"odinger operators.

On $m$-order logarithmic Schr\"odinger operator Spectral multiplier theorem for H^1 spaces associated with some S chr\"odinger operators

Reference 13

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:3a337af82a7bea4a201cf2d903abb83d0ab572f4b2a28ce2862359e3dee7405c

Observation 8ec3d74d-5673-421e-aaa1-6e737cd8940d · outbound

This paper cites odinger operators with potentials satisfying a reverse H \.

On $m$-order logarithmic Schr\"odinger operator odinger operators with potentials satisfying a reverse H \

Reference 14

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:d8f1d71295fc0eb57ca3397e4346df75f056996d7a1a5c53f129edd9776bc39f

Observation e04fe7b0-d254-4009-915e-21822adb5e11 · outbound

This paper cites odinger operators with potentials satisfying a reverse H \.

On $m$-order logarithmic Schr\"odinger operator odinger operators with potentials satisfying a reverse H \

Reference 15

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:c90ddaad756ed4fa801eceb1463aaa357a7b6e3b520266736bc4b1f54e3d8723

Observation a5f90a64-65d3-4e35-b290-b27c8bc2e4e9 · outbound

This paper cites H^p spaces for S chr\"odinger operators.

On $m$-order logarithmic Schr\"odinger operator H^p spaces for S chr\"odinger operators

Reference 16

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:bb1e8af2c5aa421cf7dc7ede5887227a9aec1a44395503d044ed4f88023faa39

Observation a668636e-2455-417b-8c7b-df86d50e8eb4 · outbound

This paper cites an unresolved cited work.

On $m$-order logarithmic Schr\"odinger operator Unresolved cited work

Reference 17

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:db0ef6773f7bf368047d8c503f26d5b71ef80af85b10f276fee8c7f7da104584

Observation 54c46956-51dd-43e8-b4d9-404e4ca20156 · outbound

This paper cites an unresolved cited work.

On $m$-order logarithmic Schr\"odinger operator Unresolved cited work

Reference 18

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:f30089d5d7e17ca5662242d12a307871d90c3a88429116e2baacec86ba19fe86

Observation 0078140c-117c-4610-a786-a23fa612ef75 · outbound

This paper cites On weighted compactness of oscillation and variation of commutators associated with S chr\"odinger operators.

On $m$-order logarithmic Schr\"odinger operator On weighted compactness of oscillation and variation of commutators associated with S chr\"odinger operators

Reference 19

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:a31cf43c050aca41117fb8950d0f2191831bbe170dfe0d2442b308729eb6093b

Observation c4e1559c-f754-42ac-a45f-7ad7877778b6 · outbound

This paper cites an unresolved cited work.

On $m$-order logarithmic Schr\"odinger operator Unresolved cited work

Reference 20

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:a98d46c7945a39ded3521a477af7759d24cf8c460f0cd4397503a48304dee093

Observation 069dfea9-5a39-434d-9172-0764dee514ba · outbound

This paper cites A new look at the fractional P oisson problem via the logarithmic L aplacian.

On $m$-order logarithmic Schr\"odinger operator A new look at the fractional P oisson problem via the logarithmic L aplacian

Reference 21

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:be5864d28b3096feefaaa617815bd2944aaacebcddaf167039bf7c118ec9d7b1

Observation 34c9a658-cd93-4ad3-8d70-774852755dd4 · outbound

This paper cites Spectral properties of the logarithmic L aplacian.

On $m$-order logarithmic Schr\"odinger operator Spectral properties of the logarithmic L aplacian

Reference 22

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:83b45ce0ecb5b619ba4109516efe4741759267e4a6c39764fcedfb19d41a3a16

Observation f9161a98-6b75-436c-bf6a-a6710a9a2a13 · outbound

This paper cites Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem.

On $m$-order logarithmic Schr\"odinger operator Fundamental Solutions of the Logarithmic Laplacian: An Approach via the Division Problem

Reference 23

Resolution
verified exact
arxiv_id, observed 2026-07-04T06:49:38.093417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:f5066ffb2f20d3cd99242264829fb2df70e2504fa79d713e7923791979e33bd5

Observation 1b38d912-e554-4712-950d-ffb997d8a92c · outbound

This paper cites An extension problem for higher order operators and operators of logarithmic type via renormalization.

On $m$-order logarithmic Schr\"odinger operator An extension problem for higher order operators and operators of logarithmic type via renormalization

Reference 24

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:bdda54273fe7856375a2d8d38a340a502d5acf8c9cf4f91c1751ff0dd5c23121

Observation c33a34dc-e502-408d-8f18-d67e7a268f00 · outbound

This paper cites Maximum principles for L aplacian and fractional L aplacian with critical integrability.

On $m$-order logarithmic Schr\"odinger operator Maximum principles for L aplacian and fractional L aplacian with critical integrability

Reference 25

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:c43b8be5f3026d345f9848787bb629b0ed01a9a2de1c16180c352e7481f802c6

Observation 1eafaf5b-fb2c-4278-be07-b804515a3e84 · outbound

This paper cites Methods of modern mathematical physics.

On $m$-order logarithmic Schr\"odinger operator Methods of modern mathematical physics

Reference 26

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:96c033bc23e801ad4a0401578d6e79b7b5b079a6ea4bc310ca78cd09ad54d99c

Observation 3ef79ec3-5677-4b0b-aa21-1495b24b639b · outbound

This paper cites an unresolved cited work.

On $m$-order logarithmic Schr\"odinger operator Unresolved cited work

Reference 27

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:c3083a20d0541386d6bcd67bdd53d273e8e0a107ab6030d621fb49d4c1217c16

Observation 4a5a9a57-7622-40d3-b0a7-440b1eff20f5 · outbound

This paper cites an unresolved cited work.

On $m$-order logarithmic Schr\"odinger operator Unresolved cited work

Reference 28

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:605a626e9af50f091c22b77d907d217574f10acf1c91f5169e793fcc2f98f80f

Observation 884c4c69-95e8-42b4-a94b-21a15cfe5c25 · outbound

This paper cites an unresolved cited work.

On $m$-order logarithmic Schr\"odinger operator Unresolved cited work

Reference 29

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:36f3629f45da0463fe380ede176a43657c3faf7dd870668d35374cd116761f18

Observation f9438f86-aac6-422f-b791-e53c6f1961b6 · outbound

This paper cites Variation operators on weighted H ardy and BMO spaces in the S chr\"odinger setting.

On $m$-order logarithmic Schr\"odinger operator Variation operators on weighted H ardy and BMO spaces in the S chr\"odinger setting

Reference 30

Resolution
unresolved
no resolver link, observed 2026-06-26T14:08:09.929477Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-26T14:08:09.929477Z digest=sha256:6491ad5b0da3549ad50503d0def10cf2169c02cb6eaa8c4f78c39a7221c6995f

Pith citing papers

No inbound Pith citation observations are available.