Paper Citation Record · LEDGER

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane

As of 17 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 1 inbound Pith citation observation for arXiv:2505.03996.

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

pith.paper-citation-record.v1
2505.03996 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T23:49:57.120937Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-31T23:20:24.744936Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

32 of 32 outbound references displayed

verified exact4
verified fuzzy18
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c830951a-0555-41af-96e6-cd11b4f14c9e · outbound

This paper cites Alessandrini, L.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Alessandrini, L

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.696109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation bc11ad65-e81a-4e80-871b-5d79f1ff5720 · outbound

This paper cites Beauchard, P.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Beauchard, P

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.679639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d64d3ac6-be41-4d04-a05f-ece7d11282af · outbound

This paper cites Beauchard and K.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Beauchard and K

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.660792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation dc39b761-a34a-4259-9ffa-bad8777301b7 · outbound

This paper cites Propagation of smallness and spectral estimates.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Propagation of smallness and spectral estimates

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-15T23:49:57.272892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation bb6399d6-21df-4a9f-8a8b-6447fe1606b9 · outbound

This paper cites Burq and I.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Burq and I

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.644864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 3ef4f2d3-c699-4167-ad16-2f70c2179dc3 · outbound

This paper cites an unresolved cited work.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:49:57.627727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 56da31ab-e439-4cc8-891e-f87adc7cd228 · outbound

This paper cites De Coster and P.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane De Coster and P

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.612444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 012afc62-b051-4007-a194-016e5bcc8f85 · outbound

This paper cites Dicke, A.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Dicke, A

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.597271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation cb4cacd4-6c3e-4323-bbff-2fbb7b3be9b5 · outbound

This paper cites Dicke, A.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Dicke, A

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.582230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 45e5fccd-8473-4d4d-97a2-a535479a2cce · outbound

This paper cites Results on gradients of harmonic functions on Lipschitz surfaces.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Results on gradients of harmonic functions on Lipschitz surfaces

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T23:49:57.013045Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 000f6dd2-ce76-4be5-ad80-88730bff01c3 · outbound

This paper cites Gagelman and H.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Gagelman and H

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.567301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e9f30593-26ce-4b14-b5ce-6d6b772d1b8a · outbound

This paper cites Jerison and G.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Jerison and G

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.552505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7ff67b73-69fe-48ee-a7ea-b30436b6423b · outbound

This paper cites Kenig, L.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Kenig, L

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.537298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 466a7a08-4b0b-4ed3-92c2-43519058c00c · outbound

This paper cites Kovrijkine.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Kovrijkine

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.521059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a80284ae-b4df-49fd-b138-2ff9b3a3d40e · outbound

This paper cites an unresolved cited work.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:49:57.504600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ec7fae96-47e5-4c87-bc98-09c26bb195b8 · outbound

This paper cites Le Rousseau, G.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Le Rousseau, G

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.488998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b36faf2f-21e8-4b3a-ab16-a83b61d2a6a6 · outbound

This paper cites Lebeau and L.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Lebeau and L

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.472803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4a7d0c88-6b59-4150-a9d3-c73aae51b49b · outbound

This paper cites an unresolved cited work.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:49:57.456932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation faeb34a3-913d-403d-823b-58c902f4c0a1 · outbound

This paper cites Logunov and E.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Logunov and E

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.442103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 28388908-4ae7-4fb9-a7a3-fca724c36644 · outbound

This paper cites Malinnikova.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Malinnikova

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.424568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d486df37-2d48-46ad-84b7-9382a88afa4f · outbound

This paper cites Spectral Inequalities For Anisotropic Shubin Operators.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Spectral Inequalities For Anisotropic Shubin Operators

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-15T23:49:57.233885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6a553bb8-7639-49ab-9479-4985ecfb6fe1 · outbound

This paper cites Martin and K.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Martin and K

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.404806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 42ccf4dd-b5d7-4f90-9ea7-ba2b733c624b · outbound

This paper cites an unresolved cited work.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:49:57.387983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 62ecd996-6c82-4ab9-8e2f-15f3857662c6 · outbound

This paper cites Naki´ c, M.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Naki´ c, M

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.371592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 31f590b7-be54-436c-84a1-4e1294d28189 · outbound

This paper cites Shubin, R.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Shubin, R

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T23:49:57.354170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 98f157e2-7d9d-4c89-9a97-79fd118d2207 · outbound

This paper cites an unresolved cited work.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:49:57.337994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1ee9ed40-1af0-4e28-93b8-dcd44274c200 · outbound

This paper cites an unresolved cited work.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:49:57.321936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 83b07674-a333-4885-9fff-a894208df280 · outbound

This paper cites an unresolved cited work.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:49:57.305598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f422f459-2977-400b-902f-b5cc81f3c1cc · outbound

This paper cites Spectral inequalities for Schr\"odinger equations with various potentials.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Spectral inequalities for Schr\"odinger equations with various potentials

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-15T23:49:57.210343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation cc3b414b-fe94-40a6-a257-51eba947da16 · outbound

This paper cites Spectral inequality for Schr\"odinger equations with power growth potentials.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Spectral inequality for Schr\"odinger equations with power growth potentials

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-15T23:49:57.110138Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2a8319f-d602-4f19-9291-d97f94e0aa6f · outbound

This paper cites Observability inequalities for heat equations with potentials.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Observability inequalities for heat equations with potentials

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-15T23:49:57.168420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2ea053b3-145f-471b-bb8c-f8978a88a7f5 · outbound

This paper cites an unresolved cited work.

Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-15T23:49:57.289212Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

Observation e675cbdd-7660-4d07-a225-66d8d81065c1 · inbound

Hausdorff type Time-Trace Observability for Airy Equations on the Line and Point Observability on the Torus cites this paper.

Hausdorff type Time-Trace Observability for Airy Equations on the Line and Point Observability on the Torus Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane

Reference 42

Resolution: unresolved; no resolver link, observed 2026-07-31T23:20:24.744936Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.