Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T05:11:57.489817Z
Paper Citation Record · LEDGER
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$
As of 22 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 1 inbound Pith citation observation for arXiv:2504.21629.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-06-27T09:32:43.371239Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-03T11:28:04.526054Z
Reference resolution
26 of 26 outbound references displayed
- verified exact1
- verified fuzzy17
- unresolved8
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation c9d71b79-d993-404d-8d64-01fef450c72c · outbound
This paper cites Alicandro and M.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Alicandro and M
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:58.041768Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 13e34755-da34-4ec9-8a89-6c8db4680a06 · outbound
This paper cites Alicandro, A.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Alicandro, A
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:58.024436Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 2e501126-1a6c-4ea4-ba65-5f6fa983d254 · outbound
This paper cites an unresolved cited work.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:11:58.006150Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation cc198249-8e4f-44aa-bbb4-c9ee5089997f · outbound
This paper cites Bollob ´as, I.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Bollob ´as, I
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.988498Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 38636829-1cf9-4bd4-95b5-70d755aee398 · outbound
This paper cites Biyikoglu, J.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Biyikoglu, J
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.969285Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 993708f6-8ebc-4eca-98f7-2240aa62a18a · outbound
This paper cites an unresolved cited work.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:11:57.950760Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation e69d8c8f-0f20-4174-888e-c9d16a2f6091 · outbound
This paper cites Brasco, G.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Brasco, G
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.931078Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation c5c67956-d176-4ef8-8139-82b71432c716 · outbound
This paper cites an unresolved cited work.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:11:57.906861Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 89782ae4-f5bd-471f-b4ad-3bbef62d049d · outbound
This paper cites Cicalese, G.P.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Cicalese, G.P
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.884530Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 6a1da66d-a8f5-488e-85e2-6562891eccce · outbound
This paper cites Cicalese, L.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Cicalese, L
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.864837Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 5faae6c7-3889-4344-b093-c418249471ac · outbound
This paper cites Dal Maso.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Dal Maso
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.845619Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 99597ddc-3e01-4704-876b-19ded3873411 · outbound
This paper cites Davoli, P.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Davoli, P
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.826357Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation d92e7c6a-15b3-4321-a76b-29b8eb279349 · outbound
This paper cites Davoli, P.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Davoli, P
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.804699Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 6a5d78f9-54ee-4f2b-a51b-cd756f83af5d · outbound
This paper cites Grigor’yan.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Grigor’yan
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.786336Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 626c208f-b577-4c53-8079-0d9239c8fce3 · outbound
This paper cites Friedrich, L.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Friedrich, L
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.767436Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation d39ed14d-5bc6-4947-b3ec-09aa42ddd46e · outbound
This paper cites Friedrich, L.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Friedrich, L
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.745924Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation f772b3ec-92ce-44d3-b674-f7fcfd1edbbf · outbound
This paper cites Fusco, F.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Fusco, F
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.723873Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 9989ebaa-b979-43b2-a5e8-381a8554f1a8 · outbound
This paper cites Hajaiej, F.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Hajaiej, F
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.703036Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 02e15cf8-2010-4714-95d3-f22d6234c3f6 · outbound
This paper cites an unresolved cited work.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:11:57.683810Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 732a4507-b4c5-4a2c-94d3-8afdb02040dc · outbound
This paper cites an unresolved cited work.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:11:57.665868Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 3ac1c7d8-969c-45bb-ac56-554ab27c89b0 · outbound
This paper cites Mainini, P.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Mainini, P
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.644421Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 60b39c33-fa52-43b8-9179-d66838610510 · outbound
This paper cites Mainini, P.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Mainini, P
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T05:11:57.623821Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation a6b8fa48-3380-467a-ae20-1c6e5c99287c · outbound
This paper cites an unresolved cited work.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:11:57.603972Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation cc67ebac-8b13-4c4d-9152-de4a6b56e851 · outbound
This paper cites an unresolved cited work.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:11:57.585106Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 4e0eb64d-824a-4b2b-8a1b-246074ddd4ee · outbound
This paper cites An Asymptotic Faber-Krahn Inequality for the Combinatorial Laplacian on Z^2.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ An Asymptotic Faber-Krahn Inequality for the Combinatorial Laplacian on Z^2
Reference 25
- Resolution
- verified exact
- local_arxiv, observed 2026-08-16T05:11:57.549570Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Observation 6b74b9f7-ac4f-49cf-ac62-175d6eba8fdc · outbound
This paper cites an unresolved cited work.
The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$ Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T05:11:57.568612Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.
Pith citing papers
Observation 93710c54-b2a3-47e1-970b-62f7bd343299 · inbound
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs cites this paper.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$
Reference 8
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T11:28:04.527374Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.