Paper Citation Record · LEDGER

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains

As of 12 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2604.20367.

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

pith.paper-citation-record.v1
2604.20367 v2

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-09T23:59:15.971149Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

41 of 41 outbound references displayed

verified exact4
verified fuzzy24
unresolved13
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e12bf905-6b94-427e-8490-7bd02153a6fb · outbound

This paper cites Agmon, On kernels, eigenvalues and eigenfunctions of operators related to elliptic problems.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Agmon, On kernels, eigenvalues and eigenfunctions of operators related to elliptic problems

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.946433Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5c603d32-9fca-47ea-95f3-0d22c00a7e41 · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:55.981487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2798f6ff-c1df-4a4c-b6a2-b6081a6af628 · outbound

This paper cites Bergweiler, A.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Bergweiler, A

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.985035Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f3357918-5bbe-4639-9500-0dd9a51d1564 · outbound

This paper cites Chavel, Eigenvalues in Riemannian Geometry.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Chavel, Eigenvalues in Riemannian Geometry

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.931832Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6966aff8-d4ca-49ef-966f-054f2dabc2eb · outbound

This paper cites Cheng, X.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Cheng, X

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.961698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 04c969c9-0bf1-447a-934b-91e5742f4107 · outbound

This paper cites Cheng, H.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Cheng, H

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.958760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 48bc8e1b-8202-4df8-b679-14e26868f632 · outbound

This paper cites Cheng, G.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Cheng, G

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.952744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 86c8c37e-3dbb-43f3-90d4-d024e652095a · outbound

This paper cites Cheng, G.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Cheng, G

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.967794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9775f7c7-2f9a-449f-847e-e2cb08e4a2cd · outbound

This paper cites Freitas, J.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Freitas, J

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.978161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5345437c-4da6-4a70-b3e6-bb17063440e9 · outbound

This paper cites Filonov, M.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Filonov, M

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.971043Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bc43d7a2-2d4b-415d-8378-e50129b88fa9 · outbound

This paper cites Filonov, M.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Filonov, M

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-11T13:51:03.838871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ca2eb12b-4233-4d62-badd-2185e44139ea · outbound

This paper cites Improved Berezin-Li-Yau inequality and Kr\"oger inequality and consequences.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Improved Berezin-Li-Yau inequality and Kr\"oger inequality and consequences

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-11T13:51:03.853985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 53c073d1-4844-41fd-b38c-82b07a1a6f5b · outbound

This paper cites P\'olya's conjecture for thin products.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains P\'olya's conjecture for thin products

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-11T13:51:03.842850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7bfb2284-79f8-4d5f-b37b-8ad49b1b3cfe · outbound

This paper cites Ivrii, Microlocal analysis and precise spectral asymptotics.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Ivrii, Microlocal analysis and precise spectral asymptotics

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.935458Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c4ac7858-aff0-4181-86f1-1faf9ca8617a · outbound

This paper cites Ivrii, The second term of the spectral asymptotics for a Laplace-Beltrami operator on manifolds with boundary.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Ivrii, The second term of the spectral asymptotics for a Laplace-Beltrami operator on manifolds with boundary

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.942938Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f6390b92-9ee5-419e-9cd9-cf09a9544d6c · outbound

This paper cites Ilyin, Lower bounds for the spectrum of the Laplace and Stokes operators.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Ilyin, Lower bounds for the spectrum of the Laplace and Stokes operators

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.964804Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f4269d95-a11f-4d5d-8c1e-9cf3f63dd69a · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:55.939523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2d030d44-325c-49ae-909b-8403f0d35686 · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:55.949602Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 617de213-414f-48cd-b9e5-d4fdc69dab8c · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:55.956037Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f58cd47c-c4ab-4cff-b3e1-ec98b446ddfb · outbound

This paper cites Deep estimates for higher eigenvalues of the poly-Laplacian.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Deep estimates for higher eigenvalues of the poly-Laplacian

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-11T13:51:03.862808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d1a854d1-b274-4c79-9fd8-a13051da54bd · outbound

This paper cites Krist\' a ly, Lord Rayleigh's conjecture for vibrating clamped plates in positively curved spaces.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Krist\' a ly, Lord Rayleigh's conjecture for vibrating clamped plates in positively curved spaces

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.974692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 60b944ff-d7bf-45ce-8f19-4ff28bb048df · outbound

This paper cites Krist\' a ly, Fundamental tones of clamped plates in nonpositively curved spaces.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Krist\' a ly, Fundamental tones of clamped plates in nonpositively curved spaces

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:56.033852Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ebb00fab-a690-4559-8c75-9286d87f2c96 · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:56.027973Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 52643c7a-8de5-4a54-8dea-5c031be2cb27 · outbound

This paper cites Kova r \' i k, S.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Kova r \' i k, S

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:56.024959Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c4e5305f-565e-409f-bb17-463587c3bb0a · outbound

This paper cites Laptv, Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces, , J.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Laptv, Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces, , J

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:56.012512Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 614c3207-1f1d-4f23-bc7e-0dc9ac1c314c · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:56.018607Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c388389d-d18f-4354-b550-f31e58fe5968 · outbound

This paper cites Lieb, The number of bound states of one-body Schr\" o dinger operators and the Weyl problem.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Lieb, The number of bound states of one-body Schr\" o dinger operators and the Weyl problem

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:56.004296Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6333c321-1b83-45ca-8ee9-a13c4eccadde · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:55.994238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 939f7a36-9466-4d3f-b2fb-da6100e0cb30 · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:55.987978Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 73e5b5f3-ec7a-4dbc-af2b-8d8db04ed372 · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:56.015420Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e4b7dec2-ad53-463b-bcd3-3f8cfdcb2035 · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:56.043423Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e7b2ddf4-44e2-4460-8bef-3efdd27a4118 · outbound

This paper cites Pleijel, On the eigenvalues and eigenfunctions of elastic plates.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Pleijel, On the eigenvalues and eigenfunctions of elastic plates

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:56.040163Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e114803e-1cf3-415d-b0fb-d68a172aaa03 · outbound

This paper cites P\' o lya, On the eigenvalues of vibrating membranes.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains P\' o lya, On the eigenvalues of vibrating membranes

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:56.001431Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation af6d5534-4990-4fce-a37c-bdd258ba65bf · outbound

This paper cites P\' o lya, G.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains P\' o lya, G

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:56.021426Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 25adf360-aede-4ce5-b2b7-0745760a7a25 · outbound

This paper cites Safarov, D.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Safarov, D

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.990780Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3d21dd85-61fb-4ffd-ac4b-442989d08c1e · outbound

This paper cites Schoen, S.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Schoen, S

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:56.009549Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 43c18343-85a2-4ab7-9591-2e40b3cd01bf · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:56.006988Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8a2b29d2-c275-4edb-a818-420687bbbe42 · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:56.046456Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5435c390-b7cf-4239-a7cd-f99b42e3e080 · outbound

This paper cites an unresolved cited work.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-05-23T12:02:56.036574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b0c664c5-513d-43aa-ba90-b685fbd54d56 · outbound

This paper cites Yildirim Yolcu, T.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Yildirim Yolcu, T

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:55.997881Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 367e4236-0d73-4437-b904-76bce6eb1e96 · outbound

This paper cites Yildirim Yolcu, T.

Improved lower bounds for Dirichlet eigenvalues of the Laplacian and poly-Laplacian on bounded Euclidean domains Yildirim Yolcu, T

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T12:02:56.030844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

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