Paper Citation Record · LEDGER

Eigenvalue gaps of the Laplacian of random graphs

As of 15 August 2026, this Paper Citation Record lists 74 of 74 outbound references and 4 inbound Pith citation observations for arXiv:2501.00234.

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

pith.paper-citation-record.v1
2501.00234 v2

Coverage vector

measured 74 of 74 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:08:06.999068Z

measured 78 of 78 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:56:06.172251Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-23T01:12:21.496443Z

Reference resolution

74 of 74 outbound references displayed

verified exact2
verified fuzzy59
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c4d41318-cb6f-4782-bf23-56e6d2c59713 · outbound

This paper cites The Surprising Power of Graph Neural Networks with Random Node Initialization.

Eigenvalue gaps of the Laplacian of random graphs The Surprising Power of Graph Neural Networks with Random Node Initialization

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T23:08:06.686691Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f36b997e-8faa-47b9-8da9-eaa4e613cd5f · outbound

This paper cites Quantum walks on graphs.

Eigenvalue gaps of the Laplacian of random graphs Quantum walks on graphs

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:08.176251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 69d229ee-e34b-4e2e-a02a-0815068b23a8 · outbound

This paper cites Anderson, Alice Guionnet, and Ofer Zeitouni.An introduction to random matrices, volume 118 ofCambridge Studies in Advanced Mathematics.

Eigenvalue gaps of the Laplacian of random graphs Anderson, Alice Guionnet, and Ofer Zeitouni.An introduction to random matrices, volume 118 ofCambridge Studies in Advanced Mathematics

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:08.160811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 1279a41c-98ca-4c25-b8b5-476fb9d7421f · outbound

This paper cites Measuring the stability of spectral clustering.

Eigenvalue gaps of the Laplacian of random graphs Measuring the stability of spectral clustering

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:08.129415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 269ba661-1cb2-4e6a-a0c5-ab4da386ec04 · outbound

This paper cites Silverstein.Spectral analysis of large dimensional random matrices.

Eigenvalue gaps of the Laplacian of random graphs Silverstein.Spectral analysis of large dimensional random matrices

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:08.103913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9842aff6-b05a-474f-bb5a-a27ae147411f · outbound

This paper cites Bandeira.

Eigenvalue gaps of the Laplacian of random graphs Bandeira

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:08.075947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a62a359d-f84a-45fd-91ec-ab4ae1ec452f · outbound

This paper cites Cambridge University Press, 2004.

Eigenvalue gaps of the Laplacian of random graphs Cambridge University Press, 2004

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:08.057371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a1ce80d8-e998-4d6c-9e78-798e0f2f466a · outbound

This paper cites Extreme gaps between eigenvalues of random matrices.Ann.

Eigenvalue gaps of the Laplacian of random graphs Extreme gaps between eigenvalues of random matrices.Ann

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:08.040599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 95ff14af-0e7f-468e-896f-6cc097e2d8db · outbound

This paper cites Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph.J.

Eigenvalue gaps of the Laplacian of random graphs Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph.J

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:08.016901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 074f109a-58d9-4546-8b17-33147210847a · outbound

This paper cites an unresolved cited work.

Eigenvalue gaps of the Laplacian of random graphs Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:08:07.994694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f7282372-7613-4c42-845a-fbc498ad3155 · outbound

This paper cites Extreme gaps between eigenvalues of Wigner matrices.J.

Eigenvalue gaps of the Laplacian of random graphs Extreme gaps between eigenvalues of Wigner matrices.J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.981522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f15fb832-d6ad-4ff9-a674-a51ce76033d8 · outbound

This paper cites Extreme eigenvalues of Laplacian random matrices with Gaussian entries.

Eigenvalue gaps of the Laplacian of random graphs Extreme eigenvalues of Laplacian random matrices with Gaussian entries

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:08:07.090702Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e8569224-c004-4625-96ca-cb7e1f51d7b1 · outbound

This paper cites The least singular value of a random symmetric matrix.Forum Math.

Eigenvalue gaps of the Laplacian of random graphs The least singular value of a random symmetric matrix.Forum Math

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.965462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 27f76222-abe4-4658-ac6b-2bf75afecb48 · outbound

This paper cites Caputo, I.

Eigenvalue gaps of the Laplacian of random graphs Caputo, I

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.951882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2eaa0326-9aee-4e95-adcd-5227430347ec · outbound

This paper cites Eigenvectors of graph Laplacians: a landscape.

Eigenvalue gaps of the Laplacian of random graphs Eigenvectors of graph Laplacians: a landscape

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:08:07.072897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a5a83236-e308-43bb-8ed6-4c02a4be2b00 · outbound

This paper cites Oscillations of networks: the role of soft nodes.Journal of Physics A: Mathematical and Theoretical, 46(3):035101, 2012.

Eigenvalue gaps of the Laplacian of random graphs Oscillations of networks: the role of soft nodes.Journal of Physics A: Mathematical and Theoretical, 46(3):035101, 2012

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.938084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 61d54838-966d-45a6-bff5-695d4cbdf790 · outbound

This paper cites Analog quantum algorithms for the mixing of Markov chains.

Eigenvalue gaps of the Laplacian of random graphs Analog quantum algorithms for the mixing of Markov chains

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.922269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4de2dd80-470c-4272-bb8d-eb3c4de8e35a · outbound

This paper cites How fast do quantum walks mix?Phys.

Eigenvalue gaps of the Laplacian of random graphs How fast do quantum walks mix?Phys

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.910483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6b689953-5c9d-4603-9420-f5f894764686 · outbound

This paper cites Academic Press, Inc., Orlando, FL, 1984.

Eigenvalue gaps of the Laplacian of random graphs Academic Press, Inc., Orlando, FL, 1984

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.896909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3a82ba1e-417c-4bb8-a611-f431a508e188 · outbound

This paper cites Estimates of the gaps between consecutive eigenvalues of Laplacian.

Eigenvalue gaps of the Laplacian of random graphs Estimates of the gaps between consecutive eigenvalues of Laplacian

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.883199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 1adbb665-46da-4564-a9c1-1f9d1c3f06fa · outbound

This paper cites Exponential algorithmic speedup by a quantum walk.

Eigenvalue gaps of the Laplacian of random graphs Exponential algorithmic speedup by a quantum walk

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.870784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 95ff27cf-39c2-4644-a528-0597e0ae3e64 · outbound

This paper cites PhD thesis, Massachusetts Institute of Technology, 2004.

Eigenvalue gaps of the Laplacian of random graphs PhD thesis, Massachusetts Institute of Technology, 2004

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.857190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5ae66856-5a86-4d38-b248-9729dd255d33 · outbound

This paper cites On the Laplacian eigenvalues ofGn,p.

Eigenvalue gaps of the Laplacian of random graphs On the Laplacian eigenvalues ofGn,p

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.843680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f626adfc-6259-4b97-9c7e-328bbc84df65 · outbound

This paper cites an unresolved cited work.

Eigenvalue gaps of the Laplacian of random graphs Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:08:07.828626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 21fb4e55-354a-4c28-bbda-4248475b0730 · outbound

This paper cites Lee, and Nathan Linial.

Eigenvalue gaps of the Laplacian of random graphs Lee, and Nathan Linial

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.805731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e5bc107d-7aab-4ea9-8e29-3741c3efc10f · outbound

This paper cites Applied numerical linear algebra.SocietyforIndustrialandAppliedMathematics(SIAM),Philadelphia, PA, 1997.

Eigenvalue gaps of the Laplacian of random graphs Applied numerical linear algebra.SocietyforIndustrialandAppliedMathematics(SIAM),Philadelphia, PA, 1997

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.787914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0e6cb2b9-eeba-46cc-8859-7d946021e625 · outbound

This paper cites Spectral distributions of adjacency and Laplacian matrices of random graphs.Ann.

Eigenvalue gaps of the Laplacian of random graphs Spectral distributions of adjacency and Laplacian matrices of random graphs.Ann

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.769717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 26558134-24a7-4b9c-9f23-df3dff5ca6f2 · outbound

This paper cites Spectral statistics of erdős-Rényi Graphs II: Eigenvalue spacing and the extreme eigenvalues.Comm.

Eigenvalue gaps of the Laplacian of random graphs Spectral statistics of erdős-Rényi Graphs II: Eigenvalue spacing and the extreme eigenvalues.Comm

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.749550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cfb1c3f9-2ea6-46bd-85ed-f91a84c57953 · outbound

This paper cites Bulk universality for generalized Wigner matrices.Probab.

Eigenvalue gaps of the Laplacian of random graphs Bulk universality for generalized Wigner matrices.Probab

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.733505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b6f8595f-d137-4ecb-afe0-24797c2d1af5 · outbound

This paper cites Small gaps of GOE.Geom.

Eigenvalue gaps of the Laplacian of random graphs Small gaps of GOE.Geom

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.710607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8625996b-fe42-4cd7-bc16-24230612005c · outbound

This paper cites Molecular graph eigenvectors for molecular coordinates: System demonstration.

Eigenvalue gaps of the Laplacian of random graphs Molecular graph eigenvectors for molecular coordinates: System demonstration

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.687471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 47e28918-e2fd-4013-8365-f0501eb70a5c · outbound

This paper cites Genericity of simple eigenvalues for a metric graph.Israel J.

Eigenvalue gaps of the Laplacian of random graphs Genericity of simple eigenvalues for a metric graph.Israel J

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.672346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6c462ee8-65a0-4879-881f-e1f030b2f14c · outbound

This paper cites Fyodorov.

Eigenvalue gaps of the Laplacian of random graphs Fyodorov

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.652824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a01dc033-0413-45f0-94f8-7b0aab097d8d · outbound

This paper cites Stability properties of graph neural networks.IEEE Trans.

Eigenvalue gaps of the Laplacian of random graphs Stability properties of graph neural networks.IEEE Trans

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.635097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f3ac7880-6033-4642-8c94-c0084664e586 · outbound

This paper cites Springer Science & Business Media, 2001.

Eigenvalue gaps of the Laplacian of random graphs Springer Science & Business Media, 2001

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-10T23:08:06.839836Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c5023b66-69d4-4c7b-9448-6e621aa6e49d · outbound

This paper cites Golub and Charles F.

Eigenvalue gaps of the Laplacian of random graphs Golub and Charles F

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.603695Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 08e5131e-f98e-4b00-b4f2-f118edb5932f · outbound

This paper cites New spectral methods for ratio cut partitioning and clustering.IEEE transactions on computer-aided design of integrated circuits and systems, 11(9):1074–1085, 1992.

Eigenvalue gaps of the Laplacian of random graphs New spectral methods for ratio cut partitioning and clustering.IEEE transactions on computer-aided design of integrated circuits and systems, 11(9):1074–1085, 1992

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-10T23:08:06.847228Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ee2445d-21b6-43b9-8f8a-42cd836c2ce5 · outbound

This paper cites A spectral approach to bandwidth and separator problems in graphs.Linear and Multilinear Algebra, 39(1-2):73–90, 1995.

Eigenvalue gaps of the Laplacian of random graphs A spectral approach to bandwidth and separator problems in graphs.Linear and Multilinear Algebra, 39(1-2):73–90, 1995

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.577106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3522a60b-9174-42cf-b365-c7df7c912244 · outbound

This paper cites Spectral statistics of sparse ő-Rényi graph Laplacians.Ann.

Eigenvalue gaps of the Laplacian of random graphs Spectral statistics of sparse ő-Rényi graph Laplacians.Ann

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.559336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d08913ac-175a-4a09-933d-1cd2ac9aeb6f · outbound

This paper cites Low eigenvalues of Laplacian matrices of large random graphs.Probab.

Eigenvalue gaps of the Laplacian of random graphs Low eigenvalues of Laplacian matrices of large random graphs.Probab

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.537730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6dda92de-ab37-44ef-9f82-c2b6054e5255 · outbound

This paper cites Quantum random walks: an introductory overview.Contemporary Physics, 44(4):307–327, 2003.

Eigenvalue gaps of the Laplacian of random graphs Quantum random walks: an introductory overview.Contemporary Physics, 44(4):307–327, 2003

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.522909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ec0bcf06-da30-4025-84dc-81064861c757 · outbound

This paper cites The expressive power of graph neural networks.Graph Neural Networks: Foundations, Frontiers, and Applications, pages 63–98, 2022.

Eigenvalue gaps of the Laplacian of random graphs The expressive power of graph neural networks.Graph Neural Networks: Foundations, Frontiers, and Applications, pages 63–98, 2022

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-10T23:08:06.867654Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 055376e1-229b-40b5-8106-3a1d538081e0 · outbound

This paper cites Distance encoding: Design provably more powerful neural networks for graph representation learning.Advances in Neural Information Processing Systems, 33:4465–4478, 2020.

Eigenvalue gaps of the Laplacian of random graphs Distance encoding: Design provably more powerful neural networks for graph representation learning.Advances in Neural Information Processing Systems, 33:4465–4478, 2020

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-10T23:08:06.871990Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 60055fb2-9331-490b-8125-4021f9b4c900 · outbound

This paper cites Litvak, Anna Lytova, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann, and Pierre Youssef.

Eigenvalue gaps of the Laplacian of random graphs Litvak, Anna Lytova, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann, and Pierre Youssef

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.474216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a2360170-d7f7-4567-ae1c-7330dd5d530c · outbound

This paper cites Tail bounds for gaps between eigenvalues of sparse random matrices.Electron.

Eigenvalue gaps of the Laplacian of random graphs Tail bounds for gaps between eigenvalues of sparse random matrices.Electron

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.459312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 273c324c-9a87-4b0b-9537-a56aed8e02bd · outbound

This paper cites Expander graphs in pure and applied mathematics.Bull.

Eigenvalue gaps of the Laplacian of random graphs Expander graphs in pure and applied mathematics.Bull

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.446900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 203ea90f-fdd2-407f-a4fc-c5c1fb6a3e60 · outbound

This paper cites Sparse random matrices have simple spectrum.Ann.

Eigenvalue gaps of the Laplacian of random graphs Sparse random matrices have simple spectrum.Ann

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.434725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b546fd29-972a-40d0-9b26-587b6cc11da1 · outbound

This paper cites Laplacian canonization: A minimalist approach to sign and basis invariant spectral embedding.Advances in Neural Information Processing Systems, 36:11296–11337, 2023.

Eigenvalue gaps of the Laplacian of random graphs Laplacian canonization: A minimalist approach to sign and basis invariant spectral embedding.Advances in Neural Information Processing Systems, 36:11296–11337, 2023

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.422854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 11f1324b-5b90-4505-a8fc-b3b6ab5ece4d · outbound

This paper cites an unresolved cited work.

Eigenvalue gaps of the Laplacian of random graphs Unresolved cited work

Reference 49

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:08:07.411992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 043ff271-2fd8-4a69-b328-fa70e254812e · outbound

This paper cites Eigenvalues in combinatorial optimization.

Eigenvalue gaps of the Laplacian of random graphs Eigenvalues in combinatorial optimization

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.391417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f68f3ec6-d2a7-403d-ae7a-b3fd7607db32 · outbound

This paper cites Restricted invertibility revisited.

Eigenvalue gaps of the Laplacian of random graphs Restricted invertibility revisited

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.373327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c113d419-0b4b-485a-9844-7a08bc00b965 · outbound

This paper cites Random matrices: tail bounds for gaps between eigenvalues.Probab.

Eigenvalue gaps of the Laplacian of random graphs Random matrices: tail bounds for gaps between eigenvalues.Probab

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.358624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 7003fdaf-d134-4ce2-b0c1-30cbfdcc5335 · outbound

This paper cites an unresolved cited work.

Eigenvalue gaps of the Laplacian of random graphs Unresolved cited work

Reference 53

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:08:07.346954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6186e7cf-3e7c-43a5-b221-2cf356aef0c0 · outbound

This paper cites Nguyen and Melanie Matchett Wood.

Eigenvalue gaps of the Laplacian of random graphs Nguyen and Melanie Matchett Wood

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.333414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation db192461-789b-4d5b-ae54-a152ba6f905f · outbound

This paper cites Local and global universality of random matrix cokernels.Mathematische Annalen, pages 1–94, 2024.

Eigenvalue gaps of the Laplacian of random graphs Local and global universality of random matrix cokernels.Mathematische Annalen, pages 1–94, 2024

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.320754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2e999a8e-ac69-4de5-a10e-b9f150aaa820 · outbound

This paper cites PhD thesis, University of Houston, 2014.

Eigenvalue gaps of the Laplacian of random graphs PhD thesis, University of Houston, 2014

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.308352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 8eb6d8db-f3ec-4fe4-b2e8-acbb5a7f418b · outbound

This paper cites an unresolved cited work.

Eigenvalue gaps of the Laplacian of random graphs Unresolved cited work

Reference 57

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:08:07.296624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4fb5776c-6c3c-47f8-a854-7a7b4611e7c6 · outbound

This paper cites The Littlewood-Offord problem and invertibility of random matrices.Adv.

Eigenvalue gaps of the Laplacian of random graphs The Littlewood-Offord problem and invertibility of random matrices.Adv

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.284784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 95d4a21f-e7e7-4cd2-9769-7ba780bc5107 · outbound

This paper cites Smallest singular value of a random rectangular matrix.Comm.

Eigenvalue gaps of the Laplacian of random graphs Smallest singular value of a random rectangular matrix.Comm

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.273210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 1bcf55ef-519a-4544-bf6a-8e335b117a12 · outbound

This paper cites No-gaps delocalization for general random matrices.

Eigenvalue gaps of the Laplacian of random graphs No-gaps delocalization for general random matrices

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.261142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e85976d5-169e-45a9-bb74-76b8bafadf59 · outbound

This paper cites Partitioning of unstructured problems for parallel processing.Computing systems in engineering, 2(2- 3):135–148, 1991.

Eigenvalue gaps of the Laplacian of random graphs Partitioning of unstructured problems for parallel processing.Computing systems in engineering, 2(2- 3):135–148, 1991

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.249467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 880138bf-e278-428b-b72f-c862a04ab679 · outbound

This paper cites The asymptotic distribution of a single eigenvalue gap of a Wigner matrix.Probab.

Eigenvalue gaps of the Laplacian of random graphs The asymptotic distribution of a single eigenvalue gap of a Wigner matrix.Probab

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.238640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 888b20df-6174-472e-bb2b-17f57e0aa483 · outbound

This paper cites Random matrices: universality of local eigenvalue statistics.Acta Math., 206(1):127–204, 2011.

Eigenvalue gaps of the Laplacian of random graphs Random matrices: universality of local eigenvalue statistics.Acta Math., 206(1):127–204, 2011

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.228571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ade163dc-06f8-477f-b601-7fb707cfc4ad · outbound

This paper cites Random matrices have simple spectrum.Combinatorica, 37(3):539–553, 2017.

Eigenvalue gaps of the Laplacian of random graphs Random matrices have simple spectrum.Combinatorica, 37(3):539–553, 2017

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.217467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d5ab6051-d458-4add-a1b7-b657f9ead61e · outbound

This paper cites Uhlenbeck.

Eigenvalue gaps of the Laplacian of random graphs Uhlenbeck

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.204291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 7f76b152-620b-43e1-9c7f-92534f924022 · outbound

This paper cites Invertibility of symmetric random matrices.Random Structures Algorithms, 44(2):135–182, 2014.

Eigenvalue gaps of the Laplacian of random graphs Invertibility of symmetric random matrices.Random Structures Algorithms, 44(2):135–182, 2014

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.192600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 068b1d77-34de-411e-9aa5-2ed7fc8d0155 · outbound

This paper cites Vinson.Closest spacing of consecutive eigenvalues.

Eigenvalue gaps of the Laplacian of random graphs Vinson.Closest spacing of consecutive eigenvalues

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.180585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4d4c01c5-6bbc-46e1-9ce1-04c07ab0f369 · outbound

This paper cites Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks.

Eigenvalue gaps of the Laplacian of random graphs Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-10T23:08:06.974752Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6edbbec1-ab40-4bc6-9fbe-15ecef40f62e · outbound

This paper cites Generic properties of Steklov eigenfunctions.Trans.

Eigenvalue gaps of the Laplacian of random graphs Generic properties of Steklov eigenfunctions.Trans

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.166944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 25995317-e5ae-4a88-b8f1-d31fadd5da44 · outbound

This paper cites Persistent Topological Laplacians -- a Survey.

Eigenvalue gaps of the Laplacian of random graphs Persistent Topological Laplacians -- a Survey

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-10T23:08:06.982622Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c20ba1c-52da-4e32-be8a-27f2e7cf5247 · outbound

This paper cites an unresolved cited work.

Eigenvalue gaps of the Laplacian of random graphs Unresolved cited work

Reference 71

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:08:07.152469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 93c9aff7-93a1-4ac0-af25-e0b2566bccd3 · outbound

This paper cites Graph neural networks: A review of methods and applications.AI open, 1:57–81, 2020.

Eigenvalue gaps of the Laplacian of random graphs Graph neural networks: A review of methods and applications.AI open, 1:57–81, 2020

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.140154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5b0f4f13-afe0-402c-8c41-b7aed3adb0d6 · outbound

This paper cites On the multiplicity one conjecture in min-max theory.Ann.

Eigenvalue gaps of the Laplacian of random graphs On the multiplicity one conjecture in min-max theory.Ann

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.128300Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ae78ed36-6996-4389-8064-bb2cd957a1f4 · outbound

This paper cites Graph convolutional neural networks via scattering.Applied and Computational Har- monic Analysis, 49(3):1046–1074, 2020.

Eigenvalue gaps of the Laplacian of random graphs Graph convolutional neural networks via scattering.Applied and Computational Har- monic Analysis, 49(3):1046–1074, 2020

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:08:07.117024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

Observation b93fa305-bb84-4ab7-9b26-bb6b8c54ae63 · inbound

The eigenvalue gap of inhomogeneous symmetric discrete random matrix cites this paper.

The eigenvalue gap of inhomogeneous symmetric discrete random matrix Eigenvalue gaps of the Laplacian of random graphs

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-23T01:12:21.498601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 76914db4-cb3e-4ff1-8607-3cbca2f1b33a · inbound

Mass-Scale Analysis of In-the-Wild Conversations Reveals Complexity Bounds on LLM Jailbreaking cites this paper.

Mass-Scale Analysis of In-the-Wild Conversations Reveals Complexity Bounds on LLM Jailbreaking Eigenvalue gaps of the Laplacian of random graphs

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T19:56:06.172251Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17bf06ce-dd9a-4fcf-805b-3a21c9c40910 · inbound

Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning cites this paper.

Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning Eigenvalue gaps of the Laplacian of random graphs

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-03T13:03:22.630485Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a3084ab-cccb-4b1e-8e62-3aa592112d15 · inbound

Dynamical phase retrieval for Schr{\"o}dinger evolution on finite graphs cites this paper.

Dynamical phase retrieval for Schr{\"o}dinger evolution on finite graphs Eigenvalue gaps of the Laplacian of random graphs

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-30T23:29:40.128476Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.