Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T11:45:37.651439Z
Paper Citation Record · LEDGER
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
As of 8 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 1 inbound Pith citation observation for arXiv:2506.02340.
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 2026-08-08T06:32:00.761636+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-06-27T02:26:48.089675Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-03T18:38:50.024532Z
Reference resolution
17 of 17 outbound references displayed
- verified exact0
- verified fuzzy14
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 9a17fcfe-5767-4aad-b253-24068e03f360 · outbound
This paper cites and Gamburd, A., 2008, Uniform expansion bounds for Cayley graphs of SL 2(Fp), Ann.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ and Gamburd, A., 2008, Uniform expansion bounds for Cayley graphs of SL 2(Fp), Ann
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:38.389942Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1521c9ad-c196-484f-9c6a-0b40176ce497 · outbound
This paper cites W., 1986, Expanders and diffusers, SIAM J.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ W., 1986, Expanders and diffusers, SIAM J
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:38.347819Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 82bfb26f-3830-409d-870b-ca6a8bfdb26d · outbound
This paper cites an unresolved cited work.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:45:38.312075Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 23394146-253e-42bb-b7b5-ffcfcd61fa8a · outbound
This paper cites and Karlsson, A., 2015, Heat kernels on regular graphs and generalized Ihara zeta function formulas, Monatsh.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ and Karlsson, A., 2015, Heat kernels on regular graphs and generalized Ihara zeta function formulas, Monatsh
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:38.273603Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ce6c209e-412c-4f02-8b4e-9b838b53d01a · outbound
This paper cites and Yau, S.-T., 1999, Coverings, heat kernels and spanning trees, Electron.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ and Yau, S.-T., 1999, Coverings, heat kernels and spanning trees, Electron
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:38.239613Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 902cbddb-cc86-480d-a565-5f66359f2ccb · outbound
This paper cites and Setti, A.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ and Setti, A
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:38.209968Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8da5fb63-11dc-42b6-a4d0-478cb291098e · outbound
This paper cites and P´ erez, A., 2022, On spectra and spectral measures of Schreier and Cayley graphs, Int.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ and P´ erez, A., 2022, On spectra and spectral measures of Schreier and Cayley graphs, Int
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:38.178794Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e190e1c0-3505-411c-b20b-8d61d265866a · outbound
This paper cites A., 2015, Growth in groups: ideas and perspectives, Bull.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ A., 2015, Growth in groups: ideas and perspectives, Bull
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:38.140037Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7dba8309-7b2e-48b1-9143-c5fc4e40ef94 · outbound
This paper cites and Smajlovi´ c, L., 2026, Constructing heat kernels on infinite graphs, Anal.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ and Smajlovi´ c, L., 2026, Constructing heat kernels on infinite graphs, Anal
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:38.113295Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5335f22b-5e47-40db-8634-1a17df001666 · outbound
This paper cites an unresolved cited work.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:45:38.077171Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 672c2f87-9530-484e-8bf2-0cd67cc1a5a0 · outbound
This paper cites Birkh¨ auser Class., Birkh¨ auser Verlag, Basel.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ Birkh¨ auser Class., Birkh¨ auser Verlag, Basel
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:38.044796Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c1da292b-2525-4df1-9fa7-bc6ae0372d1a · outbound
This paper cites R., 2024, Optimal spectral gaps, Institute for Advanced Study, Princeton, lecture, video available at https://www.ias.edu/video/optimal-spectral-gaps.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ R., 2024, Optimal spectral gaps, Institute for Advanced Study, Princeton, lecture, video available at https://www.ias.edu/video/optimal-spectral-gaps
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:38.007013Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3532682b-0803-41da-af37-189900c7a8ee · outbound
This paper cites and Rivin, I., 2010, Simplices and spectra of graphs, Discrete Comput.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ and Rivin, I., 2010, Simplices and spectra of graphs, Discrete Comput
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:37.968514Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 130f9e6f-1f3a-4318-9557-bfa0d6c04a44 · outbound
This paper cites and Sardari, N.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ and Sardari, N
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:37.930383Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 66e83908-3757-45db-85de-19ab1a8e01f6 · outbound
This paper cites and Shkredov, I.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ and Shkredov, I
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:37.889958Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 96604770-eb59-4ec9-aeda-edd9e4f57a08 · outbound
This paper cites an unresolved cited work.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:45:37.807011Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6e9dd026-f8c2-4308-98ae-31122cfd89c0 · outbound
This paper cites Math., Springer-Verlag, Berlin.
On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$ Math., Springer-Verlag, Berlin
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:45:37.721547Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Pith citing papers
Observation e0bca33b-3bb4-4c1c-81ab-5468e4fb488d · inbound
Localization of eigenfunctions in amenable unimodular random networks cites this paper.
Localization of eigenfunctions in amenable unimodular random networks On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
Reference 15
- Resolution
- verified exact
- local_arxiv, observed 2026-07-03T18:38:50.025826Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.