Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:22:03.422765Z
Paper Citation Record · LEDGER
As of 23 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 5 inbound Pith citation observations for arXiv:2507.06556.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:22:03.422765Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-15T14:22:18.970800Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-04T22:29:28.183265Z
63 of 63 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation b5e4d688-0750-455c-b54d-428ee4c0d7a1 · outbound
Spectra of high-dimensional sparse random geometric graphs Guarantees for spontaneous synchronization on random geometric graphs.SIAM Journal on Applied Dynamical Systems, 23(1):779–790, 2024
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 97459665-b586-4873-91ea-632af51ceb56 · outbound
Spectra of high-dimensional sparse random geometric graphs Expander graphs are globally synchronizing.arXiv preprint arXiv:2210.12788, 2022
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d1c0b437-cd6e-4760-8e97-52fe7a6905fe · outbound
Spectra of high-dimensional sparse random geometric graphs On the spectrum of dense random geometric graphs.The Annals of Applied Probability, 32(3):1734–1773, 2022
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 810b477a-cf50-4bd1-ac62-fbe013c4e689 · outbound
Spectra of high-dimensional sparse random geometric graphs Number 118
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f5c34f12-2729-4d8a-83dc-648b0a353ab5 · outbound
Spectra of high-dimensional sparse random geometric graphs Testing Thresholds and Spectral Properties of High-Dimensional Random Toroidal Graphs via Edgeworth-Style Expansions
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c6d8c14b-7f3b-4a6a-89af-d8db296316ad · outbound
Spectra of high-dimensional sparse random geometric graphs Springer, 2010
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9652dea6-033c-41d2-804c-ed86b40148b5 · outbound
Spectra of high-dimensional sparse random geometric graphs On the fourier coefficients of high-dimensional random geometric graphs
Reference 7
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5d634780-f3c4-4435-a35e-2be43b88d20a · outbound
Spectra of high-dimensional sparse random geometric graphs Sandwiching random geometric graphs and erdos-renyi with applications: Sharp thresholds, robust testing, and enumeration
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e07ac235-9e37-4a59-ac30-523e0b39fcd3 · outbound
Spectra of high-dimensional sparse random geometric graphs Spectral radii of sparse random matrices
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 1abe445a-e3f3-4b5d-a935-72bc7c7f41fc · outbound
Spectra of high-dimensional sparse random geometric graphs Eigenvalues of euclidean random matrices.Random Structures & Algorithms, 33(4):515–532, 2008
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation da579eb4-668d-4a68-b1d7-fe5339ddbb40 · outbound
Spectra of high-dimensional sparse random geometric graphs Resolvent of large random graphs.Random Structures & Algorithms, 37(3):332–352, 2010
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c597bc55-1383-44c1-8148-ea7f871fafa5 · outbound
Spectra of high-dimensional sparse random geometric graphs Threshold for detecting high dimensional geometry in anisotropic random geometric graphs.Random Structures & Algorithms, 64(1):125–137, 2024
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 48a3a2fc-eae1-46e0-8687-b04c39d0fb09 · outbound
Spectra of high-dimensional sparse random geometric graphs Testing for high-dimensional geometry in random graphs.Random Structures & Algorithms, 49(3):503–532, 2016
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c866f675-0b4a-4e93-a756-5a5eec39d03f · outbound
Spectra of high-dimensional sparse random geometric graphs The spectrum of random inner-product kernel matrices.Random Matrices: Theory and Applications, 2(04):1350010, 2013
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c3a9bda3-4c1a-490e-9957-642c84ccaa9f · outbound
Spectra of high-dimensional sparse random geometric graphs Scaling limit of the kuramoto model on random geometric graphs.SIAM Journal on Applied Mathematics, 85(4):1719–1748, 2025
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c3806ada-5029-4c74-a0ef-d7f4d3d8b0ab · outbound
Spectra of high-dimensional sparse random geometric graphs Christensen
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 36ee9d5b-1194-4c39-8e9c-487fcb38dcfa · outbound
Spectra of high-dimensional sparse random geometric graphs The energy landscape of the kuramoto model in random geometric graphs in a circle.SIAM Journal on Applied Dynamical Systems, 24(1):1–15, 2025
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5005026f-f381-41c5-8bba-03de657dfd80 · outbound
Spectra of high-dimensional sparse random geometric graphs Phase synchronization in random geometric graphs on the 2d sphere.arXiv preprint arXiv:2504.01151, 2025
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2dbf0590-944a-4946-aaf4-f41284beb481 · outbound
Spectra of high-dimensional sparse random geometric graphs High-dimensional random geometric graphs and their clique number.Electronic Journal of Probability, 16:2481 – 2508, 2011
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3facbb6f-24e5-4e76-ad06-30b8f26408b0 · outbound
Spectra of high-dimensional sparse random geometric graphs The spectrum of random kernel matrices: universality results for rough and varying kernels
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2f2d36b4-6b77-4a43-93a8-130715639a0b · outbound
Spectra of high-dimensional sparse random geometric graphs Synchronization in complex networks of phase oscillators: A survey.Auto- matica, 50(6):1539–1564, 2014
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d125f2b2-aa16-448b-9e92-b84adfebfc82 · outbound
Spectra of high-dimensional sparse random geometric graphs Synchronization in complex oscillator networks and smart grids.Proceedings of the National Academy of Sciences, 110(6):2005–2010, 2013
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation da56d895-6408-4226-b3f7-a09a00e97739 · outbound
Spectra of high-dimensional sparse random geometric graphs Universality for the global spectrum of random inner-product kernel matrices in the polynomial regime
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ff4d916f-5f5d-4b6d-8f53-24cba4b1ab5c · outbound
Spectra of high-dimensional sparse random geometric graphs The spectrum of kernel random matrices.Annals of statistics, 38(1):1–50, 2010
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e430d2aa-e262-4143-9415-dd522f26cb5b · outbound
Spectra of high-dimensional sparse random geometric graphs Spectra of large diluted but bushy random graphs.Random Structures & Algorithms, 49(1):160–184, 2016
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e700c5d0-5902-45f0-8d0a-500c2b4a6b93 · outbound
Spectra of high-dimensional sparse random geometric graphs Spectra of the conjugate kernel and neural tangent kernel for linear-width neural networks.Advances in neural information processing systems, 33:7710–7721, 2020
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2018b160-d656-4386-a044-02210270a593 · outbound
Spectra of high-dimensional sparse random geometric graphs Spectral techniques applied to sparse random graphs.Random Structures & Algo- rithms, 27(2):251–275, 2005
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 97b081f2-6a86-417d-8cf8-5c81fe2aab16 · outbound
Spectra of high-dimensional sparse random geometric graphs American Mathematical Soc., 2008
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 441abdd2-f818-4d3d-9dc2-31cadc289574 · outbound
Spectra of high-dimensional sparse random geometric graphs Global law of conjugate kernel random matrices with heavy-tailed weights
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9f322d96-5615-40cc-ab2e-10cc673abea4 · outbound
Spectra of high-dimensional sparse random geometric graphs On the normalized laplacian spectra of random geometric graphs.Journal of Theoretical Probability, 36(1):46–77, 2023
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c115a4af-22c0-4471-8cd7-dde1a919fae3 · outbound
Spectra of high-dimensional sparse random geometric graphs Fitting a geometric graph to a protein–protein inter- action network.Bioinformatics, 24(8):1093–1099, 2008
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 1538c8f3-b39f-4f1b-801c-7c5ca769372d · outbound
Spectra of high-dimensional sparse random geometric graphs Latent space approaches to social network analysis
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation db967e79-bfa3-4d2a-b7d7-3a1e25b1aae8 · outbound
Spectra of high-dimensional sparse random geometric graphs Algorithm 447: efficient algorithms for graph manipulation.Communications of the ACM, 16(6):372–378, 1973
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 6190889d-1fbd-477a-ab9d-42c272ae3141 · outbound
Spectra of high-dimensional sparse random geometric graphs The random graph process is globally synchronizing
Reference 34
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3afcde75-1195-4ac2-8e55-c0c464dacc57 · outbound
Spectra of high-dimensional sparse random geometric graphs On spectral radii of unraveled balls.Journal of Combinatorial Theory, Series B, 136:72–80, 2019
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7d74f66d-bc04-487a-ad23-78e7b4c34985 · outbound
Spectra of high-dimensional sparse random geometric graphs Delocalization and limiting spectral distribution of erd˝ os-r´ enyi graphs with constant expected degree.Electronic Communications in Probability, 2018
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4c81f92c-6713-46aa-a22c-33f337c59297 · outbound
Spectra of high-dimensional sparse random geometric graphs Sufficiently dense kuramoto networks are globally synchronizing.Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(7), 2021
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 54fafc0a-da22-4433-8768-a981af92e446 · outbound
Spectra of high-dimensional sparse random geometric graphs A global synchronization theorem for oscillators on a random graph.Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(9), 2022
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3fa2e780-eb52-4185-ab24-b73f72ece4e1 · outbound
Spectra of high-dimensional sparse random geometric graphs Self-entrainment of a population of coupled non-linear oscillators
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 1648c873-52c5-4582-8c24-e67de05c6356 · outbound
Spectra of high-dimensional sparse random geometric graphs Concentration and regularization of random graphs.Random Structures & Algorithms, 51(3):538–561, 2017
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 17cfd398-6b5b-4e71-9d77-504df9a8c54e · outbound
Spectra of high-dimensional sparse random geometric graphs Spectral clustering in the Gaussian mixture block model
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation be8b8344-24ee-4079-aaf8-995e01a071c4 · outbound
Spectra of high-dimensional sparse random geometric graphs On the landscape of synchronization networks: A perspective from nonconvex optimization.SIAM Journal on Optimization, 29(3):1879–1907, 2019
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 80c6f337-49dd-48ed-a30f-013a6f9d259c · outbound
Spectra of high-dimensional sparse random geometric graphs Testing thresholds for high-dimensional sparse random geometric graphs
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d5044279-74de-42ba-8b30-aaa066e8bc07 · outbound
Spectra of high-dimensional sparse random geometric graphs Local and global expansion in random geo- metric graphs
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e2039aad-a51f-4b71-9a91-ed84413af671 · outbound
Spectra of high-dimensional sparse random geometric graphs A probabilistic view of latent space graphs and phase transitions.Bernoulli, 29(3):2417–2441, 2023
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation ce00e135-d961-4dfc-ad59-d2631048334e · outbound
Spectra of high-dimensional sparse random geometric graphs A random matrix approach to neural networks.The Annals of Applied Probability, 28(2):1190–1248, 2018
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 60689c8c-821e-49b9-9e17-90278ad98495 · outbound
Spectra of high-dimensional sparse random geometric graphs An equivalence principle for the spectrum of random inner-product kernel matrices with polynomial scalings.The Annals of Applied Probability, 35(4):2411–2470, 2025
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8a24a9a3-6abf-4f23-989d-f10e030c424d · outbound
Spectra of high-dimensional sparse random geometric graphs Impossibility of latent inner product recovery via rate distortion
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 30f99735-3195-4040-82df-628269292a1e · outbound
Spectra of high-dimensional sparse random geometric graphs Connectivity of large wireless networks under a general connection model.IEEE transactions on information theory, 59(3):1761–1772, 2012
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5a716d35-2baa-4117-8bff-d1e68112f51f · outbound
Spectra of high-dimensional sparse random geometric graphs Parallel ear decomposition search (eds) and st-numbering in graphs.Theoretical Computer Science, 47:277–298, 1986
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b49f8f76-d6cb-4c4a-be79-40f2ce7618a7 · outbound
Spectra of high-dimensional sparse random geometric graphs Generalization error of random feature and kernel methods: hypercontractivity and kernel matrix concentration.Applied and Computational Harmonic Analysis, 59:3–84, 2022
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 69d62bcc-7695-4a61-b084-09e4b865412e · outbound
Spectra of high-dimensional sparse random geometric graphs Universality of kernel random matrices and kernel regression in the quadratic regime.arXiv preprint arXiv:2408.01062, 2024
Reference 52
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b74cb78e-15c5-461e-bafd-2412c24e25f9 · outbound
Spectra of high-dimensional sparse random geometric graphs Nonlinear random matrix theory for deep learning.Advances in neural information processing systems, 30, 2017
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 0dc0cc92-93cb-4e32-8bad-2fd774d18f95 · outbound
Spectra of high-dimensional sparse random geometric graphs Oxford University Press, 2003
Reference 54
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 610ccf65-b6dc-4854-b11f-7ce5a1f42d5b · outbound
Spectra of high-dimensional sparse random geometric graphs Basic models and questions in statistical network analysis.Statistics Surveys, 11:1–47, 2017
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 14b970ac-64ca-45ec-bc93-0873a4ab2fd8 · outbound
Spectra of high-dimensional sparse random geometric graphs A theorem on graphs, with an application to a problem of traffic control.The American Mathematical Monthly, 46(5):281–283, 1939
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 43fa513f-32c7-47df-9e21-21988b26f3cd · outbound
Spectra of high-dimensional sparse random geometric graphs The kuramoto model in complex networks.Physics Reports, 610:1–98, 2016
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 476c60ab-d04e-4015-8173-1e106f5941fb · outbound
Spectra of high-dimensional sparse random geometric graphs Enumerative combinatorics volume 1 second edition.Cambridge studies in advanced mathe- matics, 2011
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4dca6394-6992-4a3f-915f-4b38057feee1 · outbound
Spectra of high-dimensional sparse random geometric graphs There is no non-zero stable fixed point for dense networks in the homogeneous kuramoto model
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 42144ed5-9031-4d3e-bb85-409e58e6343e · outbound
Spectra of high-dimensional sparse random geometric graphs Sparse random graphs: Eigenvalues and eigenvectors.Random Structures & Algorithms, 42(1):110–134, 2013
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d98a2980-4404-4f95-8ea6-10fc01eeeb21 · outbound
Spectra of high-dimensional sparse random geometric graphs Spectral norm of random matrices.Combinatorica, 27(6):721–736, 2007
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7ffa8ba1-75b1-4d8a-9f77-d7c55d0838a6 · outbound
Spectra of high-dimensional sparse random geometric graphs Deformed semicircle law and concentration of nonlinear random matrices for ultra-wide neural networks.The Annals of Applied Probability, 34(2):1896–1947, 2024
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c153b812-8101-42b2-bfea-f1dfeb00ba7a · outbound
Spectra of high-dimensional sparse random geometric graphs A graphon approach to limiting spectral distributions of wigner-type matrices.Random Structures & Algorithms, 56(1):251–279, 2020
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 73314c54-0221-4ddf-b6ce-23295ae7effc · inbound
On the edge eigenvalues of sparse random geometric graphs Spectra of high-dimensional sparse random geometric graphs
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 50e0f246-dabd-4e59-aa6b-083dbc9cd8fc · inbound
Spectral Concentration and Recovery in Sparse High-Dimensional Random Geometric Graphs Spectra of high-dimensional sparse random geometric graphs
Reference 2016
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f7037ddc-6c79-48fe-981a-829fe3d8b837 · inbound
Distinguishability threshold for random geometric graphs Spectra of high-dimensional sparse random geometric graphs
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a63bbd50-91ef-4d57-a71a-da7567715a1a · inbound
Majority Dynamics on Resampled Sparse Erd\H{o}s--R\'enyi Graphs: Gaussian Winner Selection and Pace to Unanimity Spectra of high-dimensional sparse random geometric graphs
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b1f6efc8-9bc5-49ea-834b-62977d444ce7 · inbound
Spectral graph clustering with inhomogeneous latent geometry Spectra of high-dimensional sparse random geometric graphs
Reference 9
Source-reported events for the cited work
Unavailable: canonical work link unavailable.