Paper Citation Record · LEDGER

Central limit theorems for the eigenvalues of graph Laplacians on data clouds

As of 17 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 1 inbound Pith citation observation for arXiv:2507.18803.

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

pith.paper-citation-record.v1
2507.18803 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:23:00.217880Z

measured 50 of 50 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T22:29:25.505207Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-04T22:29:28.019913Z

Reference resolution

49 of 49 outbound references displayed

verified exact1
verified fuzzy21
unresolved27
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation af8dd327-482d-47b4-8959-1df4ed5369aa · outbound

This paper cites Ando and T.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Ando and T

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.733848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c1caaf7b-4352-4f9d-a0e6-0934a8cab80f · outbound

This paper cites Athreya, J.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Athreya, J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.724048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 795af28d-1558-41d6-813f-09e0e844b01a · outbound

This paper cites Athreya, D.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Athreya, D

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.713922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fa8d5273-628a-4e9c-a54d-440a5156c9ab · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.704123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9ca4357c-6751-4b3f-94f4-1ef314ca55d4 · outbound

This paper cites Belkin and P.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Belkin and P

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T18:23:00.065731Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d1c989e-943f-4771-9bcf-f7393355de86 · outbound

This paper cites Belkin and P.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Belkin and P

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.687502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5af7aa1d-3fb7-49f6-bb39-89fd3569357e · outbound

This paper cites Belkin, P.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Belkin, P

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.677666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0719d0d7-a529-4605-a6d6-ede02c3b9b9c · outbound

This paper cites Biskup, R.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Biskup, R

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.666853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5a4fc769-5a0b-4ea0-800b-8752e15228b8 · outbound

This paper cites Bousquet, U.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Bousquet, U

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.655206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 649890d9-f0ab-47d8-8c81-8bfda647b848 · outbound

This paper cites Bretagnolle and C.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Bretagnolle and C

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.644194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d85f30e3-b775-462f-a311-9972e63f5d5f · outbound

This paper cites Burago, S.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Burago, S

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.633024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c7917521-85d6-46e0-9e5a-559e84b39685 · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.622423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9ab265f1-5a6f-4956-9a90-220b6f56f473 · outbound

This paper cites Calder and N.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Calder and N

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.611138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d205f479-d42e-4666-bb17-62a459a57e5a · outbound

This paper cites Calder, N.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Calder, N

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.598473Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 19f00f1d-36c9-4ffe-8799-625fe1c88e8a · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.589097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 354085c7-1a6c-4506-90d6-4bdd62ef82ae · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.579505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 80ba8e67-e831-4039-86a0-fbabc99eb8c7 · outbound

This paper cites Cheng and N.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Cheng and N

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.569593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1d78a616-24cc-403f-9472-02110dcc8682 · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.559706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 95cd5e93-0cfc-4d4c-af1e-263d770fd445 · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T18:23:00.117801Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 668d5a50-5d3a-42f9-8d56-c42388e27e8f · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.542852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ed19ba29-fd09-4407-8140-2a103572919e · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.532385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3be7c410-e44d-4519-9301-c8997a1a2b71 · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.522103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5d05a454-3e57-497c-8e58-1ac0b4e41cd7 · outbound

This paper cites Fern´ andez-Real and X.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Fern´ andez-Real and X

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.512232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 42357c8a-7a7d-4cb3-820e-ec5d746833a4 · outbound

This paper cites Garc´ ıa Trillos, M.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Garc´ ıa Trillos, M

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.501802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c55c3e79-189e-4f55-9f72-2a5cc199a5ac · outbound

This paper cites Garc´ ıa Trillos, P.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Garc´ ıa Trillos, P

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-15T18:23:00.135101Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c020f4f1-d251-4598-b722-418dbaaafffa · outbound

This paper cites Garc´ ıa Trillos and D.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Garc´ ıa Trillos and D

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.485344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 88bc7dda-4da9-4afd-a363-0d023162c6c0 · outbound

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

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T18:23:00.141132Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42607908-8180-4918-b6dd-9693a0f27add · outbound

This paper cites Gin´ e and V.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Gin´ e and V

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.475264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6f11d277-848a-46cd-ad81-c95575e99690 · outbound

This paper cites Gu and J.-C.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Gu and J.-C

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.464811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7e63515d-7343-44b1-9dc4-19390b5addbc · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.452599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 358290f9-eba0-4389-aa43-5b29f902490c · outbound

This paper cites Hein, J.-Y.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Hein, J.-Y

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.442410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 82107a4a-4d60-4ed8-8196-5ba24d9a63ef · outbound

This paper cites Hein, J.-Y.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Hein, J.-Y

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.432380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ae78ad97-ee88-46e9-84ae-5cc2697db4e1 · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.421758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5c6553fe-25cb-4299-8a20-ce1ecafae8d4 · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.411728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c8d98e10-ff4a-4128-98e4-db12f55683e4 · outbound

This paper cites Consistency of augmentation graph and network approximability in contrastive learning.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Consistency of augmentation graph and network approximability in contrastive learning

Reference 35

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:23:00.275328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b3894e92-b4a3-49b6-8d25-a535c6725a93 · outbound

This paper cites Spectral Neural Networks: Approximation Theory and Optimization Landscape.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Spectral Neural Networks: Approximation Theory and Optimization Landscape

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-15T18:23:00.172097Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7713167e-b233-42b7-bbae-47aeaf0492ab · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.401315Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3c33b1e0-5852-451d-907f-a6ba4893b503 · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.390620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1e0aa506-2358-4228-95f6-98a6c35dcd5c · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.379596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7c18f904-db08-4279-a8fa-2eba7fbe9ec0 · outbound

This paper cites Santambrogio.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Santambrogio

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-15T18:23:00.185754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7d8ffe9f-6683-4eac-8e2d-c7c873444837 · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-15T18:23:00.189280Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4e8da561-355f-46ca-9088-8e7e67be9134 · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.355794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f7b66bba-efc3-4cb8-91f5-e93d339d6d6f · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.345026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 49aee9f9-b36b-44e5-932b-fb0276f2f029 · outbound

This paper cites Eigenvector fluctuations and limit results for random graphs with infinite rank kernels.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Eigenvector fluctuations and limit results for random graphs with infinite rank kernels

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-15T18:23:00.199602Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ba144e6-5567-4640-9990-a23ce2bb6f86 · outbound

This paper cites Tang and C.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Tang and C

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.334189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 80e73793-46ae-459b-b0c0-527adfca1724 · outbound

This paper cites Tao and Z.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Tao and Z

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-15T18:23:00.206885Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c9d6051-b826-4346-925f-8b1a105e4f2f · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.315759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 90a15600-5d5c-4def-82cb-4c646d03bef3 · outbound

This paper cites Von Luxburg.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Von Luxburg

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:23:00.305850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1d2e5d19-925b-4959-bf87-695c8806fdae · outbound

This paper cites an unresolved cited work.

Central limit theorems for the eigenvalues of graph Laplacians on data clouds Unresolved cited work

Reference 49

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:23:00.296430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

Observation 0661a6ad-5cbe-40e7-b307-7210e4c188d0 · inbound

On the edge eigenvalues of sparse random geometric graphs cites this paper.

On the edge eigenvalues of sparse random geometric graphs Central limit theorems for the eigenvalues of graph Laplacians on data clouds

Reference 42

Resolution: verified exact; local_arxiv, observed 2026-08-04T22:29:28.073135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.