Paper Citation Record · LEDGER

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs

As of 21 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2411.11071.

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pith.paper-citation-record.v1
2411.11071 v1

Coverage vector

measured 36 of 36 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-12T19:10:34.698863Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

36 of 36 outbound references displayed

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External citation measurements

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Outbound references

Observation ce1d031a-a52e-46e1-968a-17d489853dc1 · outbound

This paper cites On kernels, eigenvalues, and eigenfuncti ons of operators related to elliptic problems.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs On kernels, eigenvalues, and eigenfuncti ons of operators related to elliptic problems

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.201580Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2d4c782e-9aaa-416e-81af-5d7a5a238501 · outbound

This paper cites Eigenvalue sum estimates for lattice subgraphs.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Eigenvalue sum estimates for lattice subgraphs

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.191280Z

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Observation 6506e578-2114-4b91-8982-4fd5ec6e01b6 · outbound

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Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Unresolved cited work

Reference 3

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Observation 4bb2430f-1ea8-4377-b7f1-34364e1345ef · outbound

This paper cites Asymptotic behavior of the sp ectrum of diﬀerential equations.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Asymptotic behavior of the sp ectrum of diﬀerential equations

Reference 4

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Observation 8e08e486-0cf1-4c18-a82b-80d6d701c09d · outbound

This paper cites an unresolved cited work.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Unresolved cited work

Reference 5

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Observation 8ac3b95b-d888-4aef-b40e-088b7231497b · outbound

This paper cites A lower boun d for eigenvalues of the poly-Laplacian with arbitrary order.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs A lower boun d for eigenvalues of the poly-Laplacian with arbitrary order

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.151054Z

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Observation dff944cf-13b6-4c3e-a3e3-f9d8fa360097 · outbound

This paper cites Upper and lower bounds fo r eigenvalues of the clamped plate problem.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Upper and lower bounds fo r eigenvalues of the clamped plate problem

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.139529Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 637013cd-07b9-438f-be7a-21e2a3db035c · outbound

This paper cites Diﬀerence equations of polyharmon ic type.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Diﬀerence equations of polyharmon ic type

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.129139Z

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Observation 61f277dc-4b41-4305-a3d1-eae7d7ed06fc · outbound

This paper cites Discrete bi-laplacians and bi harmonic b-splines.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Discrete bi-laplacians and bi harmonic b-splines

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.118574Z

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Observation 83a01439-aa26-405e-9d4a-75d72282e150 · outbound

This paper cites Lieb-Thirring inequalities for higher order diﬀerential operators.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Lieb-Thirring inequalities for higher order diﬀerential operators

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.108030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0121e744-df61-4e7c-9e18-955a7408330a · outbound

This paper cites Polyharmonic bound- ary value problems , volume 1991 of Lecture Notes in Mathematics.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Polyharmonic bound- ary value problems , volume 1991 of Lecture Notes in Mathematics

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.098085Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fbcca447-29cc-4cdc-8b52-110272372aa5 · outbound

This paper cites The laplacian spec- trum of a graph.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs The laplacian spec- trum of a graph

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.088003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3efbcfc4-4217-496b-a405-7a477f0b53b2 · outbound

This paper cites Graph embeddings an d laplacian eigenvalues.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Graph embeddings an d laplacian eigenvalues

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.077051Z

Source-reported events for the cited work

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Observation b168f03c-92d9-4a5a-96cb-4f3ecb9471ce · outbound

This paper cites Extremum problems for eigenvalues of elliptic operators.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Extremum problems for eigenvalues of elliptic operators

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.066586Z

Source-reported events for the cited work

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Observation 56b325ac-3b76-40d0-b9e0-89c41040402e · outbound

This paper cites Laplace and bi-la place equations for directed networks and markov chains.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Laplace and bi-la place equations for directed networks and markov chains

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.056015Z

Source-reported events for the cited work

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Observation 6378701a-e6ea-4c7d-a5a7-f659423e14d3 · outbound

This paper cites Harmonic functions of gen eral graph laplacians.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Harmonic functions of gen eral graph laplacians

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.043918Z

Source-reported events for the cited work

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Observation 3a4be6ed-3241-480e-8495-fec98e720ba3 · outbound

This paper cites Universal bounds for eigenvalues of the polyharmonic operators.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Universal bounds for eigenvalues of the polyharmonic operators

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:35.032437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8f408530-21f1-4e69-a4c0-ab4b9279aeba · outbound

This paper cites Expansion of eigenvalues of rank-one perturbations of the discrete bilaplacian.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Expansion of eigenvalues of rank-one perturbations of the discrete bilaplacian

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-12T19:10:34.744331Z

Source-reported events for the cited work

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Observation 6c759a18-0c26-4fa8-b4d2-2fc533b117f8 · outbound

This paper cites Two- dimensional Berezin-Li- Yau inequalities with a correction term.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Two- dimensional Berezin-Li- Yau inequalities with a correction term

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.926536Z

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Observation e668fef8-95b0-4415-a140-95ae29e007fb · outbound

This paper cites Kr¨ oger.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Kr¨ oger

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.916231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 51978313-171f-4ad3-9a3b-f1c3dd855429 · outbound

This paper cites Estimates for sums of eigenvalues of the Laplacian.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Estimates for sums of eigenvalues of the Laplacian

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.906084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7b414f68-2cde-4102-bec7-88ee558da3a5 · outbound

This paper cites ´Equations aux D´ eriv´ ees Partielles.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs ´Equations aux D´ eriv´ ees Partielles

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.894990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9d26276a-7cc4-4b2e-9e05-769f91639389 · outbound

This paper cites an unresolved cited work.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-12T19:10:34.884429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e202820d-542e-4524-a8db-05045a572310 · outbound

This paper cites On the Schr¨ odinger equatio n and the eigenvalue prob- lem.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs On the Schr¨ odinger equatio n and the eigenvalue prob- lem

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.874468Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4a2927c8-5143-4bdf-9789-75eab2d2f9a9 · outbound

This paper cites an unresolved cited work.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-12T19:10:34.863807Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6e226cee-fd77-47c6-95ef-7b380500751a · outbound

This paper cites an unresolved cited work.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-12T19:10:34.853076Z

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Observation 7a23a029-1f99-4761-a1e9-b9d494ca7165 · outbound

This paper cites Netrusov and T.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Netrusov and T

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.843071Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 28f9f71f-dcce-40eb-b258-310e013d40cd · outbound

This paper cites On the eigenvalues and eigenfunctions of elast ic plates.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs On the eigenvalues and eigenfunctions of elast ic plates

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.832894Z

Source-reported events for the cited work

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Observation 5ba15d38-6f78-46b4-a452-cc9b9ef01d61 · outbound

This paper cites an unresolved cited work.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-12T19:10:34.822591Z

Source-reported events for the cited work

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Observation 31c15571-5874-48f8-962d-fa6cc52dfa64 · outbound

This paper cites On the membrane model and the discrete Bilaplacian.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs On the membrane model and the discrete Bilaplacian

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.811992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f86e9c68-cce3-45f8-b047-e6733026ef52 · outbound

This paper cites Strichartz.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Strichartz

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.801132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0a90724d-a0d2-4390-bf06-7e86cb6c337a · outbound

This paper cites Eigenvalue estimates for the fractional Laplacian on lattice subgraphs.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Eigenvalue estimates for the fractional Laplacian on lattice subgraphs

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-12T19:10:34.683723Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10db5772-29e2-47fa-8092-aff3c5cabfaf · outbound

This paper cites Estimates for eigenvalu es of poly-harmonic opera- tors.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Estimates for eigenvalu es of poly-harmonic opera- tors

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.789217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ae3a42bf-819e-426d-97ff-cb68bea3be74 · outbound

This paper cites Das asymptotische Verteilungsgesetz de r Eigenwerte linearer par- tieller Diﬀerentialgleichungen (mit einer Anwendung auf d ie Theorie der Hohlraum- strahlung).

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Das asymptotische Verteilungsgesetz de r Eigenwerte linearer par- tieller Diﬀerentialgleichungen (mit einer Anwendung auf d ie Theorie der Hohlraum- strahlung)

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.778632Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 46e0cd20-aee8-48c1-a52c-cbe5255dadf3 · outbound

This paper cites Eigenvalue bounds for the poly-harmonic operators.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Eigenvalue bounds for the poly-harmonic operators

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.767862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0ef0388a-2c97-4b8a-a00a-d8ab287c5765 · outbound

This paper cites Multidimensio nal lower bounds for the eigenvalues of Stokes and Dirichlet Laplacian operators.

Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs Multidimensio nal lower bounds for the eigenvalues of Stokes and Dirichlet Laplacian operators

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T19:10:34.756609Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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