Paper Citation Record · LEDGER

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs

As of 20 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 1 inbound Pith citation observation for arXiv:2506.07694.

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

pith.paper-citation-record.v1
2506.07694 v1

Coverage vector

measured 39 of 39 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:41:01.304565Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T11:44:04.909610Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T11:44:04.990750Z

Reference resolution

39 of 39 outbound references displayed

verified exact1
verified fuzzy27
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1cc0e6d6-7c4c-4fe3-a57f-ba46fed63b8b · outbound

This paper cites Adams, Sobolev spaces, Pure Appl.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Adams, Sobolev spaces, Pure Appl

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.796366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9de9b976-abc9-4078-b16e-7a604c663258 · outbound

This paper cites Scuola Norm.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Scuola Norm

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.784453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 94a2d8cb-6609-48a7-be9e-28869b2cff85 · outbound

This paper cites Ambrosetti, P.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Ambrosetti, P

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.772571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5b6ee3c2-0335-47cb-970d-afdda05b7997 · outbound

This paper cites Baleanu, K.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Baleanu, K

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.760815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6c4b50e2-c61c-4be3-bc7a-02637f1a3d54 · outbound

This paper cites Bogdan, T.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Bogdan, T

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.749312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3d7b3c5e-e1d1-415d-b071-0f10f32a9d96 · outbound

This paper cites Brezis, P.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Brezis, P

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.737862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 446b83b7-b5d9-46b2-ab4e-33fa051d7b83 · outbound

This paper cites Ciaurri, C.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Ciaurri, C

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.726753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2b3a3f67-1403-412b-ab8d-156753dc5658 · outbound

This paper cites Ciaurri, L.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Ciaurri, L

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.715568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 552d4a5f-8b67-4a37-b55b-e3228fe7c01a · outbound

This paper cites De Coster, S.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs De Coster, S

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.703838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 14d167a2-42a8-42d9-af75-02c93d0aed37 · outbound

This paper cites del Teso, D.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs del Teso, D

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.691884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b6390662-baa0-4705-ba96-dff2f9b548b7 · outbound

This paper cites Di Nezza, G.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Di Nezza, G

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.680150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 17a62f53-4fbb-4624-b246-966039620003 · outbound

This paper cites Ge, Kazdan-Warner equation on graph in the negative case, J.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Ge, Kazdan-Warner equation on graph in the negative case, J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.669001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 664d6db1-37b3-4275-a330-01ed6d633130 · outbound

This paper cites Getoor, First passage times for symmetric stable processes in space, Trans.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Getoor, First passage times for symmetric stable processes in space, Trans

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.657455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e9aafdac-8cf9-4497-8acb-a9798228dfeb · outbound

This paper cites Grigor’yan, Y.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Grigor’yan, Y

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.646040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation fc2484d1-e156-4854-9bc6-9acb2886cd81 · outbound

This paper cites Grigor’yan, Y.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Grigor’yan, Y

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.634455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5c22800f-bcf3-4e97-8595-8cc98ef7d9a0 · outbound

This paper cites Grigor’yan, Y.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Grigor’yan, Y

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.622954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 541c41c4-a38d-4fd0-9b56-91737f89b602 · outbound

This paper cites Haeseler, M.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Haeseler, M

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.610359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1b83cb2f-42eb-4496-99fe-2b621adf0497 · outbound

This paper cites an unresolved cited work.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:41:01.596952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation baf0e2f5-b290-4393-9a0b-837a0b7645ea · outbound

This paper cites an unresolved cited work.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:41:01.584737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 80fe8f41-a86c-455b-a5e8-4a952459d1d3 · outbound

This paper cites an unresolved cited work.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:41:01.572811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ba8b13b5-54c9-462b-836c-2089fb0d9c06 · outbound

This paper cites Huang, On stochastic completeness of weighted graphs, PhD thesis, Bielefeld Uni- versity, 2011.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Huang, On stochastic completeness of weighted graphs, PhD thesis, Bielefeld Uni- versity, 2011

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.561222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 747053dc-a318-4a59-98e7-f5394718bef4 · outbound

This paper cites Keller, D.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Keller, D

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.548742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 68626494-f1e5-49b3-a981-fd4f0fcd2282 · outbound

This paper cites Keller, D.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Keller, D

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T05:41:01.247920Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a831097b-53cd-4535-a88d-8563468732a7 · outbound

This paper cites Keller, M.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Keller, M

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.527466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f9db3a22-e61e-4b5a-929f-746dd0391065 · outbound

This paper cites Kwa ´snicki, Ten equivalent definitions of the fractional laplace operator, Fract.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Kwa ´snicki, Ten equivalent definitions of the fractional laplace operator, Fract

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.514658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 810011ee-087c-428f-9477-3a8e3d1af385 · outbound

This paper cites an unresolved cited work.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:41:01.502492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e5b7f9ab-ad50-47fa-847c-96686a51089f · outbound

This paper cites an unresolved cited work.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:41:01.489902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 0500514a-51f8-4406-99f2-8c8ac0576891 · outbound

This paper cites Lizama, M.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Lizama, M

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.476736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 73fa4f4a-edba-4608-bf92-77cd3ce242f0 · outbound

This paper cites Lizama, L.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Lizama, L

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.464855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9bf806e0-531d-464f-85e7-c0033ff9ddc8 · outbound

This paper cites an unresolved cited work.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:41:01.452842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9a7ca908-3ba5-414b-835b-1b6e75bfa3ec · outbound

This paper cites Runst, W.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Runst, W

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.441074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a3f53e07-ddf7-49d0-93a4-042ed654f6e7 · outbound

This paper cites an unresolved cited work.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:41:01.429187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c541f2a8-d178-4c2d-9cc0-5252ca39c565 · outbound

This paper cites Existence and convergence of solutions to $p$-Laplace equations on locally finite graphs.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Existence and convergence of solutions to $p$-Laplace equations on locally finite graphs

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:41:01.370931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e8707d34-d3c0-42f5-bf4f-c3e755707d1b · outbound

This paper cites an unresolved cited work.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-07T05:41:01.286955Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a1e365f-8033-48f0-b910-d9a93b3e3e27 · outbound

This paper cites Valdinoci, From the long jump random walk to the fractional Laplacian, Bol.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Valdinoci, From the long jump random walk to the fractional Laplacian, Bol

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.408543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 75b340c3-c8dc-4c18-94cb-54c595cf7d88 · outbound

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

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Eigenvalue estimates for the fractional Laplacian on lattice subgraphs

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-07T05:41:01.293785Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 096d5c3e-f3e1-403f-a01d-9292f489cfea · outbound

This paper cites Wojciechowski, Heat kernel and essential spectrum of infinite graphs, Indiana Univ.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Wojciechowski, Heat kernel and essential spectrum of infinite graphs, Indiana Univ

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.395914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2ffebc9a-fd1e-42e5-8126-73f05db9c1e4 · outbound

This paper cites Fractional Laplace operator and related Schr\"odinger equations on locally finite graphs.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Fractional Laplace operator and related Schr\"odinger equations on locally finite graphs

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-07T05:41:01.300882Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 712c7c1a-d1f0-4286-9f94-65b4c0f1c6d2 · outbound

This paper cites Zhang, L.

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs Zhang, L

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:41:01.383664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation 830c235c-47fa-4321-ba79-0a88a03c565a · inbound

Positive solutions to fractional $p$-Laplacian Choquard equation on lattice graphs cites this paper.

Positive solutions to fractional $p$-Laplacian Choquard equation on lattice graphs Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs

Reference 39

Resolution: verified exact; local_arxiv, observed 2026-08-06T11:44:04.997963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.