Paper Citation Record · LEDGER

Uniform Sobolev inequalities on geometric graphs

As of 7 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2607.16948.

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

pith.paper-citation-record.v1
2607.16948 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T19:37:55.620521Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

38 of 38 outbound references displayed

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Outbound references

Observation 6d6e6cf9-b20c-4945-a471-63d5a58e08d4 · outbound

This paper cites Adams and John J.

Uniform Sobolev inequalities on geometric graphs Adams and John J

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:52.095289Z

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Unavailable: canonical work link unavailable.

Observation 8cccc16a-e618-4a23-931a-18ab739c7c4b · outbound

This paper cites A non-local anisotropic model for phase transitions: asymptotic behaviour of rescaled energies.European J.

Uniform Sobolev inequalities on geometric graphs A non-local anisotropic model for phase transitions: asymptotic behaviour of rescaled energies.European J

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:52.216904Z

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Observation 466535d4-e7ad-4c71-a195-a7f9824c2a44 · outbound

This paper cites Asymptotic behavior of the Dirichlet energy on Poisson point clouds.J.

Uniform Sobolev inequalities on geometric graphs Asymptotic behavior of the Dirichlet energy on Poisson point clouds.J

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:52.392865Z

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Observation 71b6151d-6db6-4fa9-936a-ef8f113d348e · outbound

This paper cites Mumford–Shah functionals on graphs and their asymptotics.Nonlinearity, 33(8):3846–3888, 2020.

Uniform Sobolev inequalities on geometric graphs Mumford–Shah functionals on graphs and their asymptotics.Nonlinearity, 33(8):3846–3888, 2020

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:52.518854Z

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Observation 0855d09f-6eb2-4b69-8c77-a31f9eb8c3b8 · outbound

This paper cites The∞-Wasserstein distance: local solutions and existence of optimal transport maps.SIAM J.

Uniform Sobolev inequalities on geometric graphs The∞-Wasserstein distance: local solutions and existence of optimal transport maps.SIAM J

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:52.656760Z

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Observation 5fad3654-03b6-4a29-8e64-80188c505e1c · outbound

This paper cites an unresolved cited work.

Uniform Sobolev inequalities on geometric graphs Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:52.768547Z

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Observation ecf14c37-73cd-43fe-8dab-bb2e2bcf095c · outbound

This paper cites an unresolved cited work.

Uniform Sobolev inequalities on geometric graphs Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:52.880701Z

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Observation 0d8bc387-f853-440b-b820-759abcbf2022 · outbound

This paper cites Large data limit for a phase transition model with the p-Laplacian on point clouds.European J.

Uniform Sobolev inequalities on geometric graphs Large data limit for a phase transition model with the p-Laplacian on point clouds.European J

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:52.963327Z

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Observation 85d717ef-992f-462d-848a-b0785b286198 · outbound

This paper cites Birkh¨ auser Boston, Inc., Boston, MA, 1993.

Uniform Sobolev inequalities on geometric graphs Birkh¨ auser Boston, Inc., Boston, MA, 1993

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:53.053181Z

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Observation e7ea5f55-a373-4377-9048-44dcd225a3fc · outbound

This paper cites Consistency of modularity clustering on random geometric graphs.Ann.

Uniform Sobolev inequalities on geometric graphs Consistency of modularity clustering on random geometric graphs.Ann

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:53.175535Z

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Observation b73585ad-2e4e-4e54-a7d6-dd47670263c6 · outbound

This paper cites Dunlop, Dejan Slepˇ cev, Andrew M.

Uniform Sobolev inequalities on geometric graphs Dunlop, Dejan Slepˇ cev, Andrew M

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:53.289407Z

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Observation e270ed12-a125-4a43-bdca-f5065fe54c10 · outbound

This paper cites Evans and Ronald F.

Uniform Sobolev inequalities on geometric graphs Evans and Ronald F

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:53.418901Z

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Observation a490c9d4-b1e3-43bc-a355-cd16d5287c43 · outbound

This paper cites Variational analysis of discrete Dirichlet problems in periodically perforated domains.ESAIM Control Optim.

Uniform Sobolev inequalities on geometric graphs Variational analysis of discrete Dirichlet problems in periodically perforated domains.ESAIM Control Optim

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:53.555374Z

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Observation 364b3729-05db-4aed-ac23-45a31c469ee2 · outbound

This paper cites Error estimates for spectral convergence of the graph Laplacian on random geometric graphs toward the Laplace- Beltrami operator.Found.

Uniform Sobolev inequalities on geometric graphs Error estimates for spectral convergence of the graph Laplacian on random geometric graphs toward the Laplace- Beltrami operator.Found

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:53.669995Z

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Observation a2a04bc3-1813-4728-87c7-bf42a0aea122 · outbound

This paper cites On the consistency of graph-based Bayesian semi-supervised learning and the scalability of sampling algorithms.J.

Uniform Sobolev inequalities on geometric graphs On the consistency of graph-based Bayesian semi-supervised learning and the scalability of sampling algorithms.J

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:53.780168Z

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Observation 0c221848-6233-4d8c-a7e6-052b7953104e · outbound

This paper cites Continuum limits of posteriors in graph Bayesian inverse problems.SIAM J.

Uniform Sobolev inequalities on geometric graphs Continuum limits of posteriors in graph Bayesian inverse problems.SIAM J

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:53.876689Z

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Observation 084d68a7-8702-4700-8951-956476812718 · outbound

This paper cites On the rate of convergence of empirical measures in ∞-transportation distance.Canad.

Uniform Sobolev inequalities on geometric graphs On the rate of convergence of empirical measures in ∞-transportation distance.Canad

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:53.946267Z

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Observation a23b5da9-f4d2-4cf8-a7cb-d53dae95599e · outbound

This paper cites Continuum limit of total variation on point clouds.

Uniform Sobolev inequalities on geometric graphs Continuum limit of total variation on point clouds

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.010512Z

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Observation 61eae21e-c0bb-4156-838e-084219162356 · outbound

This paper cites A variational approach to the consistency of spectral clustering.Appl.

Uniform Sobolev inequalities on geometric graphs A variational approach to the consistency of spectral clustering.Appl

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.066119Z

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Observation cea45224-f4aa-4da9-9604-151145c1af3d · outbound

This paper cites Estimating perimeter using graph cuts.Adv.

Uniform Sobolev inequalities on geometric graphs Estimating perimeter using graph cuts.Adv

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.113699Z

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Observation 1de20285-8ffa-4501-a9d0-3eb4ffcf3335 · outbound

This paper cites Consistency of Cheeger and ratio graph cuts.J.

Uniform Sobolev inequalities on geometric graphs Consistency of Cheeger and ratio graph cuts.J

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.168979Z

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Observation 21ccb909-5645-4b56-941f-38b38064b97b · outbound

This paper cites Grisvard.Elliptic problems in nonsmooth domains, volume 24 ofMonographs and Studies in Mathematics.

Uniform Sobolev inequalities on geometric graphs Grisvard.Elliptic problems in nonsmooth domains, volume 24 ofMonographs and Studies in Mathematics

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.216824Z

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Observation c6555a17-1cec-4766-a957-c2e73fe6feb1 · outbound

This paper cites an unresolved cited work.

Uniform Sobolev inequalities on geometric graphs Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.271611Z

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Observation 3d0b5434-d9f0-41a9-afa9-11939ad88fa7 · outbound

This paper cites Lee.Introduction to smooth manifolds, volume 218 ofGraduate Texts in Mathematics.

Uniform Sobolev inequalities on geometric graphs Lee.Introduction to smooth manifolds, volume 218 ofGraduate Texts in Mathematics

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.325570Z

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Observation 4484b935-884d-4b59-a1a3-5cdad7bd93fd · outbound

This paper cites American Mathematical Society, Providence, RI, 2009.

Uniform Sobolev inequalities on geometric graphs American Mathematical Society, Providence, RI, 2009

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.419352Z

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Observation f640311f-6473-486f-8750-7c92c529902e · outbound

This paper cites an unresolved cited work.

Uniform Sobolev inequalities on geometric graphs Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.500095Z

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Observation c48cbd3c-2d6c-4f19-bd04-5f0fb94247ce · outbound

This paper cites PhD thesis, Technische Universiteit Delft, Delft, Netherlands, in prep.

Uniform Sobolev inequalities on geometric graphs PhD thesis, Technische Universiteit Delft, Delft, Netherlands, in prep

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.576689Z

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Observation 578dcdd4-1605-4a09-9b61-c61ae8043165 · outbound

This paper cites An extension to Banach stackings of the Brezis–Pazy semigroup-convergence theorem, with applications toλ-convex gradient flows.

Uniform Sobolev inequalities on geometric graphs An extension to Banach stackings of the Brezis–Pazy semigroup-convergence theorem, with applications toλ-convex gradient flows

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.627845Z

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Observation ec6bc318-7de7-4e63-808f-f1cbd13df539 · outbound

This paper cites Uniform graph sobolev inequalities and graph gradient flows: convergence from discrete to continuum.

Uniform Sobolev inequalities on geometric graphs Uniform graph sobolev inequalities and graph gradient flows: convergence from discrete to continuum

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.701029Z

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Observation 1b073cef-bdfb-4e0d-acab-e84230486a0e · outbound

This paper cites Consistency of Dirichlet partitions.SIAM J.

Uniform Sobolev inequalities on geometric graphs Consistency of Dirichlet partitions.SIAM J

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.771953Z

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Observation a64617fa-d5b8-45f1-a257-8cf8f04cdac4 · outbound

This paper cites Oxford University Press, Oxford, 2003.

Uniform Sobolev inequalities on geometric graphs Oxford University Press, Oxford, 2003

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.847278Z

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Observation 4a33a5cf-5dd6-437a-a050-9f5fa5825c9d · outbound

This paper cites Analysis ofp-Laplacian regularization in semisupervised learning.SIAM J.

Uniform Sobolev inequalities on geometric graphs Analysis ofp-Laplacian regularization in semisupervised learning.SIAM J

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.885946Z

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Observation 0560d09c-28d2-4238-9e8e-311d92c55b4c · outbound

This paper cites Rohde, and Dejan Slepˇ cev.

Uniform Sobolev inequalities on geometric graphs Rohde, and Dejan Slepˇ cev

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.889858Z

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Observation 8783143a-fff5-4ef0-b4d6-1ca99476a5e7 · outbound

This paper cites Asymptotic analysis of the Ginzburg–Landau functional on point clouds.Proc.

Uniform Sobolev inequalities on geometric graphs Asymptotic analysis of the Ginzburg–Landau functional on point clouds.Proc

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:54.950585Z

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Observation c35caf19-cb0f-4d6b-ba4d-bcef40f9e8af · outbound

This paper cites Deep limits of residual neural networks.Res.

Uniform Sobolev inequalities on geometric graphs Deep limits of residual neural networks.Res

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:55.123494Z

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Observation 2bd0dd51-5417-4236-8489-f242f8cd8ef8 · outbound

This paper cites Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds.

Uniform Sobolev inequalities on geometric graphs Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:55.246487Z

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Observation 2a487a89-343d-475d-8791-8c58476d38c8 · outbound

This paper cites Bertozzi.

Uniform Sobolev inequalities on geometric graphs Bertozzi

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:55.426603Z

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Observation c4a1a049-729b-4bdd-adff-28583de21064 · outbound

This paper cites Springer, Berlin, Heidelberg, first edition, 2009.

Uniform Sobolev inequalities on geometric graphs Springer, Berlin, Heidelberg, first edition, 2009

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-01T19:37:55.620521Z

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