Paper Citation Record · LEDGER

The existence and upper bound for stable photon spheres in static spherically symmetric black holes

As of 20 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2508.19823.

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

pith.paper-citation-record.v1
2508.19823 v2

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T15:39:28.543654Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T09:17:01.105026Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

27 of 27 outbound references displayed

verified exact6
verified fuzzy1
unresolved18
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3536fffe-d5c5-4f29-9811-218a0f8e2e05 · outbound

This paper cites Schwarzschild black hole lensing.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Schwarzschild black hole lensing

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.326838Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21c7172b-dbf1-401b-bb9f-f61eec1923ff · outbound

This paper cites Connection between black-hole quasinormal modes and lensing in the strong deflection limit.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Connection between black-hole quasinormal modes and lensing in the strong deflection limit

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.337809Z

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Observation 70a9c9fd-bb86-433b-97b6-d049c22348f0 · outbound

This paper cites Is the gravitational-wave ringdown a probe of the event horizon?.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Is the gravitational-wave ringdown a probe of the event horizon?

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.347228Z

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Observation faff876b-813a-4e0d-98b0-6fc38948722b · outbound

This paper cites First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.354054Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0cf5b472-48c2-4005-98f1-d32f2724f5ed · outbound

This paper cites Upper bound on the radii of black-hole photonspheres.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Upper bound on the radii of black-hole photonspheres

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.362667Z

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Observation 6bf37d8e-7a04-45a5-bb8b-ef294e2d891b · outbound

This paper cites Photon Spheres and Sonic Horizons in Black Holes from Supergravity and Other Theories.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Photon Spheres and Sonic Horizons in Black Holes from Supergravity and Other Theories

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.369545Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8236c16-f2b9-4d7c-8c26-66013e7d095f · outbound

This paper cites The fastest way to circle a black hole.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes The fastest way to circle a black hole

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.376163Z

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Unavailable: canonical work link unavailable.

Observation 63d80898-3573-4148-8547-08d8a818f4fd · outbound

This paper cites Lower bound on the radii of black-hole photonspheres.

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 047d2b31-9925-44c4-a4a9-c9cc74defef7 · outbound

This paper cites Upper bounds on the compactness at the innermost light ring of anisotropic horizonless spheres.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Upper bounds on the compactness at the innermost light ring of anisotropic horizonless spheres

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:39:29.547890Z

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 a9458c8a-a544-47f5-93a8-ee9b0f72eb33 · outbound

This paper cites Lower bound on the radii of light rings in traceless black-hole spacetimes.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Lower bound on the radii of light rings in traceless black-hole spacetimes

Reference 10

Resolution: metadata mismatch; local_arxiv, observed 2026-08-05T15:39:29.484727Z

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 865bc352-b6cb-4ed6-9bb1-3a2123117ed5 · outbound

This paper cites Upper bound on the radius of the innermost photonsphere in the regular compact star spacetime.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Upper bound on the radius of the innermost photonsphere in the regular compact star spacetime

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:39:29.422358Z

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 5adb6f0b-d4a2-4f8d-a898-00edebc76735 · outbound

This paper cites Can light-rings self-gravitate?.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Can light-rings self-gravitate?

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.426259Z

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Observation 8e5c441d-9890-43f7-9129-52db5a81cbf1 · outbound

This paper cites Can different black holes cast the same shadow?.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Can different black holes cast the same shadow?

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.432298Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1c3c0cca-f99a-4ca3-9d69-dbd37fa3662d · outbound

This paper cites Quasi-topological Electromagnetism: Dark Energy, Dyonic Black Holes, Stable Photon Spheres and Hidden Electromagnetic Duality.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Quasi-topological Electromagnetism: Dark Energy, Dyonic Black Holes, Stable Photon Spheres and Hidden Electromagnetic Duality

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.439500Z

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Unavailable: canonical work link unavailable.

Observation 4d10ea76-cf14-4ff8-92c4-2a46e477a979 · outbound

This paper cites On the Size of a Black Hole: The Schwarzschild is the Biggest.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes On the Size of a Black Hole: The Schwarzschild is the Biggest

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.446383Z

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Observation 03f16f63-8a53-4abf-bbc7-06178bda7fbe · outbound

This paper cites On the Size of Rotating Black Holes.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes On the Size of Rotating Black Holes

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:39:29.228177Z

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 00049cba-8ff8-45be-9f2e-4a02834570a8 · outbound

This paper cites Universal bounds on the size of a black hole.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Universal bounds on the size of a black hole

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:39:29.184292Z

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 df6f8ebd-a74d-48d9-868c-c1789365e74a · outbound

This paper cites Stationary black holes and light rings.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Stationary black holes and light rings

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.471810Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0bdbfa44-ed38-4227-966b-e5b33fbf2bdb · outbound

This paper cites Topological Charge and Black Hole Photon Spheres.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Topological Charge and Black Hole Photon Spheres

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.476610Z

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Unavailable: canonical work link unavailable.

Observation aa645a3f-82cc-4eec-ac19-5ff016ad8565 · outbound

This paper cites an unresolved cited work.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Unresolved cited work

Reference 20

Resolution: metadata mismatch; raw_fallback, observed 2026-08-05T15:39:29.073567Z

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 e0a6cc7b-b572-4a44-937f-fd2490e9bfbf · outbound

This paper cites Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.490945Z

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Observation 6cdec149-49b6-4351-9def-c6b2d2e938f4 · outbound

This paper cites Hairy black holes in the XX-th and XXI-st centuries.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Hairy black holes in the XX-th and XXI-st centuries

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.500122Z

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Unavailable: canonical work link unavailable.

Observation bb1676ef-4e7a-4125-b23b-4735d91914b2 · outbound

This paper cites Bondi, Mon.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Bondi, Mon

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T15:39:29.910901Z

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 812169f7-14e5-47b6-ae3c-5424e0a84fd9 · outbound

This paper cites If vacuum energy can be negative, why is mass always positive?: Uses of the subdominant trace energy condition.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes If vacuum energy can be negative, why is mass always positive?: Uses of the subdominant trace energy condition

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-05T15:39:28.866924Z

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 4b9f473c-714d-43e3-a9ce-ddc5929e3c69 · outbound

This paper cites Black holes have no short hair.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Black holes have no short hair

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.529008Z

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Unavailable: canonical work link unavailable.

Observation 6add9c13-f600-473d-9d3b-bd7d9b9b5294 · outbound

This paper cites Cosmology with a stiff matter era.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Cosmology with a stiff matter era

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.535542Z

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Unavailable: canonical work link unavailable.

Observation 23356bbf-ea7f-44d0-874e-75e86b52d9df · outbound

This paper cites an unresolved cited work.

The existence and upper bound for stable photon spheres in static spherically symmetric black holes Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-05T15:39:28.543654Z

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Unavailable: canonical work link unavailable.

Pith citing papers

Observation 3bfaba0c-da4a-4bb5-875b-8715ea04962d · 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 The existence and upper bound for stable photon spheres in static spherically symmetric black holes

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T09:17:01.105026Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.