Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
On the sharpness of a three circles theorem for discrete harmonic functions
As of 19 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:1512.03732.
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 2026-08-19T06:32:44.657259+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-14T10:40:55.405685Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-14T10:40:55.522574Z
Reference resolution
0 of 0 outbound references displayed
- verified exact0
- verified fuzzy0
- unresolved0
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
No outbound reference observations are available for this paper version.
Pith citing papers
Observation 04cb0fb9-b117-4447-9ff7-2868e9a8eea0 · inbound
A Liouville principle for the random conductance model under degenerate conditions cites this paper.
A Liouville principle for the random conductance model under degenerate conditions On the sharpness of a three circles theorem for discrete harmonic functions
Reference 32
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T10:40:55.527051Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.