Paper Citation Record · LEDGER

The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis

As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 7 inbound Pith citation observations for arXiv:2407.14035.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2407.14035 v5

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 7 of 7 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T05:46:10.868927Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-18T14:42:41.986244Z

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 e1a9d83f-c4d2-422a-a09c-88a3775e1d4a · inbound

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions cites this paper.

Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-05T05:46:10.868927Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76d29bc2-cdda-4829-ab9c-52458c8678ea · inbound

Black Hole Gravitational Phenomena in Higher-Order Curvature-Scalar Gravity cites this paper.

Black Hole Gravitational Phenomena in Higher-Order Curvature-Scalar Gravity The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis

Reference 211

Resolution: unresolved; no resolver link, observed 2026-08-04T16:49:20.190674Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e073a949-fa73-40cb-be5f-fc407ee462d7 · inbound

The Flight of the Bumblebee in a Non-Commutative Geometry: A New Black Hole Solution cites this paper.

The Flight of the Bumblebee in a Non-Commutative Geometry: A New Black Hole Solution The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis

Reference 75

Resolution: verified exact; arxiv_id, observed 2026-05-18T14:42:41.992169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4601e097-28e1-4a9c-a55b-7488e32a5e35 · inbound

Light propagation and quasinormal modes of a topologically charged Schwarzschild-Klinkhamer wormhole cites this paper.

Light propagation and quasinormal modes of a topologically charged Schwarzschild-Klinkhamer wormhole The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis

Reference 99

Resolution: unresolved; no resolver link, observed 2026-08-03T08:48:41.927207Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d2e07671-0a81-44ea-a60a-217fef70d014 · inbound

Photon Spheres and shadow of modified black-hole entropies cites this paper.

Photon Spheres and shadow of modified black-hole entropies The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-11T16:01:05.650210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8dedbdf8-d60e-4927-bd06-1a498409f66f · inbound

Photon Spheres and shadow of modified black-hole entropies cites this paper.

Photon Spheres and shadow of modified black-hole entropies The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-12T07:51:28.148269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7377c59a-7977-440e-9c6e-57afd0db42e9 · inbound

Photon Spheres and shadow of modified black-hole entropies cites this paper.

Photon Spheres and shadow of modified black-hole entropies The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-14T21:39:28.987302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.