Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T11:44:48.483671Z
Paper Citation Record · LEDGER
Ancient caloric functions and parabolic frequency on graphs
As of 23 August 2026, this Paper Citation Record lists 4 of 4 outbound references and 0 inbound Pith citation observations for arXiv:2412.15145.
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 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
4 of 4 outbound references displayed
- verified exact1
- verified fuzzy3
- unresolved0
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 4d8da48a-048b-4cc2-a4db-b47a04a0cdde · outbound
This paper cites an unresolved cited work.
Ancient caloric functions and parabolic frequency on graphs Unresolved cited work
Reference 1
- Resolution
- verified exact
- doi, observed 2026-08-11T11:44:48.578729Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation cf42f0dc-0f6b-4f7f-8432-5dbc3f99c0e1 · outbound
This paper cites Kleiner, A new proof of Gromov’s theorem on groups of polynomial growt h, J.
Ancient caloric functions and parabolic frequency on graphs Kleiner, A new proof of Gromov’s theorem on groups of polynomial growt h, J
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T11:44:48.525117Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 16f7f26d-0889-4b59-b203-411ac0d6ade6 · outbound
This paper cites Hang and F.
Ancient caloric functions and parabolic frequency on graphs Hang and F
Reference 2018
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T11:44:48.560146Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5a53a01e-286a-4554-9035-74a4c997372b · outbound
This paper cites Hua and J.
Ancient caloric functions and parabolic frequency on graphs Hua and J
Reference 4039
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T11:44:48.542430Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Pith citing papers
No inbound Pith citation observations are available.