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Paper Citation Record · LEDGER

Gravitational Lensing by Black Holes with Multiple Photon Spheres

As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:2204.13948.

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

pith.paper-citation-record.v1
2204.13948 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 5 of 5 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 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:42:33.197737Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T09:46:01.088461Z

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 0532b2c9-8767-4019-b32a-71d616a94c80 · inbound

Spin-induced Scalarized Black Holes in Einstein-Maxwell-scalar Models cites this paper.

Spin-induced Scalarized Black Holes in Einstein-Maxwell-scalar Models Gravitational Lensing by Black Holes with Multiple Photon Spheres

Reference 43

Resolution
malformed identifier
no resolver link, observed 2026-08-07T11:42:33.197737Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T11:42:33.197737Z digest=sha256:6c00a014c13b953971bb2f85570a0aaefd6447810331d347d85f2456c879a849

Observation 050ac179-feeb-43d0-b76f-d9030ba5e09f · inbound

Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres cites this paper.

Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres Gravitational Lensing by Black Holes with Multiple Photon Spheres

Reference 84

Resolution
unresolved
no resolver link, observed 2026-08-06T16:40:23.286384Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T16:40:23.286384Z digest=sha256:b4539ce9c3364abc5d74e311d844c3e305ba420ad50124db4d96077d37ef4412

Observation 397458d2-667b-4998-803b-18e8f90201cf · inbound

Critical Behavior of Photon Rings in Kerr-Bertotti-Robinson Spacetime cites this paper.

Critical Behavior of Photon Rings in Kerr-Bertotti-Robinson Spacetime Gravitational Lensing by Black Holes with Multiple Photon Spheres

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-02T17:32:16.177329Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-02T17:32:16.177329Z digest=sha256:a7c8f7cc1b4173aae7db1e0aa1556e1aea1871d1f337cfdd55cdf7db32eedb45

Observation e51bd735-7cff-47c8-b772-3c11d0d626e7 · inbound

Optical Appearance of Scalarized Kerr-Newman Black Holes with Multiple Light Rings cites this paper.

Optical Appearance of Scalarized Kerr-Newman Black Holes with Multiple Light Rings Gravitational Lensing by Black Holes with Multiple Photon Spheres

Reference 82

Resolution
malformed identifier
arxiv_id, observed 2026-05-11T09:46:01.090960Z

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.

source=pdf_text observed=2026-05-10T15:51:17.908867Z digest=sha256:e621c77f3c77c0dee84548dc6aae88fae87bc84a34c85c5b418ec71a0c5c1e13

Observation 9d3f63e1-2e00-4422-bdaa-916fde028171 · inbound

Topologically equivalent yet radiatively distinct orbits in EMRI system cites this paper.

Topologically equivalent yet radiatively distinct orbits in EMRI system Gravitational Lensing by Black Holes with Multiple Photon Spheres

Reference 15

Resolution
verified exact
arxiv_id, observed 2026-05-10T13:05:24.514835Z

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.

source=pdf_text observed=2026-05-10T13:04:39.993350Z digest=sha256:908f2e783efa8ad6944300b4a958ca1f61672a6f8ef070bc4fe991327954c6eb