Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T20:00:44.761346Z
Paper Citation Record · LEDGER
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion
As of 14 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2501.09693.
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 2026-08-14T06:32:32.682623+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-07T21:34:01.616572Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-07T21:34:02.110747Z
Reference resolution
30 of 30 outbound references displayed
- verified exact3
- verified fuzzy15
- unresolved12
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b11fbc60-5443-4267-bd5f-869f96681d4d · outbound
This paper cites Becker, F.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Becker, F
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.445742Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation e247c43e-31ed-4627-8032-8a97f8ee8813 · outbound
This paper cites van den Berg and E.B.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion van den Berg and E.B
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.418525Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 1419bb60-0e55-433d-8fe9-0575382b83f2 · outbound
This paper cites Berkolaiko and P.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Berkolaiko and P
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.399560Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 1f3b6d61-2772-4687-b115-e22e5c287608 · outbound
This paper cites Bifulco and D.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Bifulco and D
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.382631Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f79ad1bf-b21b-4ffa-9721-43c43fc09659 · outbound
This paper cites On the Lipschitz continuity of the heat kernel.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion On the Lipschitz continuity of the heat kernel
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-10T20:00:44.599806Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b746d091-6adc-4022-94b9-d659dcf564e4 · outbound
This paper cites Bifulco and D.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Bifulco and D
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.367116Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation a65dc539-93aa-4206-8d60-176e9b4f4fda · outbound
This paper cites Sticky Brownian motions on star graphs.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Sticky Brownian motions on star graphs
Reference 7
- Resolution
- verified exact
- local_arxiv, observed 2026-08-10T20:00:44.962588Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 031d5118-c920-49c0-8799-acd19e5b5198 · outbound
This paper cites Borthwick, E.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Borthwick, E
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.351892Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation a0804681-3fe3-422c-a5f4-12e8109c88ba · outbound
This paper cites Burchard and S.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Burchard and S
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.336392Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ed16481b-6a7c-474c-a829-937382fb1913 · outbound
This paper cites Cattaneo.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Cattaneo
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.318914Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation dc5e66be-ec36-4ce4-94e4-f72554407781 · outbound
This paper cites Düfel, J.B.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Düfel, J.B
Reference 11
- Resolution
- verified exact
- raw_fallback, observed 2026-08-10T20:00:44.938482Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 822aa734-1a2b-457e-8f3a-45193cc04181 · outbound
This paper cites an unresolved cited work.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:00:45.303540Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation cf3dee74-646b-434e-895b-df5d946be31c · outbound
This paper cites Friedlander.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Friedlander
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.286298Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 5ab6fb14-9070-470d-8768-50922ec7409a · outbound
This paper cites an unresolved cited work.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:00:45.269066Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 699bc6ae-fda2-4940-a190-e555c2fd5866 · outbound
This paper cites Karatzas and S.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Karatzas and S
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.252680Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 877f5aac-34ce-47f0-9bb5-7efa24fbf4df · outbound
This paper cites Kostenko, D.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Kostenko, D
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.236676Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 6a39c596-5130-4717-9457-c912ecc30663 · outbound
This paper cites Kostrykin, J.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Kostrykin, J
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.221104Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3f810a85-49ec-49a3-89ae-e9f6b1f7412e · outbound
This paper cites Kostrykin, J.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Kostrykin, J
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.205093Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation be72aa0e-9b32-47cd-870f-c0aaa91919dc · outbound
This paper cites an unresolved cited work.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:00:45.188285Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 62aee019-5dc7-4aca-873f-a5899f2f4b60 · outbound
This paper cites Kurasov and S.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Kurasov and S
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.172024Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation fd5786f1-3b72-4eae-981c-467b3eaeece4 · outbound
This paper cites an unresolved cited work.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:00:45.156000Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 661459f1-3ade-4c4e-9535-d47e3c8a11c5 · outbound
This paper cites an unresolved cited work.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:00:45.139840Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c01da5cd-3588-444e-bb61-8ecdc5e403eb · outbound
This paper cites an unresolved cited work.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:00:45.117249Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation bb0aed0a-8a51-4e89-a0bf-50fc8b1dffec · outbound
This paper cites Mugnolo and M.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Mugnolo and M
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T20:00:45.095975Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation a5e62f86-de67-408c-bc78-c405a4642ce8 · outbound
This paper cites an unresolved cited work.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:00:45.076592Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation cc335ada-b1ac-417e-8351-975400bb34c8 · outbound
This paper cites Torsional Rigidity on Metric Graphs with Delta-Vertex Conditions.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Torsional Rigidity on Metric Graphs with Delta-Vertex Conditions
Reference 26
- Resolution
- verified exact
- local_arxiv, observed 2026-08-10T20:00:44.814739Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation d809f505-2a7d-4775-b9c2-7380ee9c0fe9 · outbound
This paper cites an unresolved cited work.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:00:45.059808Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 2ebd7338-4a15-4726-aa00-e6c00a3b721e · outbound
This paper cites an unresolved cited work.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:00:45.039617Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c473cffe-1578-4012-8e74-053ce293413a · outbound
This paper cites an unresolved cited work.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:00:45.021401Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ce6a0ef4-3ee6-477a-8a2b-d43dc34ab3cc · outbound
This paper cites an unresolved cited work.
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T20:00:44.998335Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Pith citing papers
Observation 704b7b76-d7f6-478f-9070-a07106935058 · inbound
On the heat content of compact quantum graphs cites this paper.
On the heat content of compact quantum graphs Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion
Reference 14
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T21:34:02.117460Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.