Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
Lower bound on the radii of black-hole photonspheres
As of 20 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2012.03962.
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 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-16T01:22:13.048633Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-05T15:39:29.582372Z
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 008f5692-efa3-4b6b-9670-5ac0801c5a70 · inbound
Bounds for Lyapunov exponent of circular light orbits in black holes cites this paper.
Bounds for Lyapunov exponent of circular light orbits in black holes Lower bound on the radii of black-hole photonspheres
Reference 66
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T16:21:20.280610Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1bcc236e-5018-4908-b668-127fb29b476d · inbound
Upper bound on the radius of the innermost stable circular orbit of black holes cites this paper.
Upper bound on the radius of the innermost stable circular orbit of black holes Lower bound on the radii of black-hole photonspheres
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T01:22:13.048633Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 63d80898-3573-4148-8547-08d8a818f4fd · inbound
The existence and upper bound for stable photon spheres in static spherically symmetric black holes cites this paper.
The existence and upper bound for stable photon spheres in static spherically symmetric black holes Lower bound on the radii of black-hole photonspheres
Reference 8
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T15:39:29.591634Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 886aef37-9bf7-4ea7-adcb-899160887628 · inbound
Static spheres in black hole spacetimes: pairing, energy conditions, and an upper bound on the innermost radius cites this paper.
Static spheres in black hole spacetimes: pairing, energy conditions, and an upper bound on the innermost radius Lower bound on the radii of black-hole photonspheres
Reference 20
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T09:17:01.119989Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.