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Paper Citation Record · LEDGER

Investigating strong gravitational lensing effects by suppermassive black holes with Horndeski gravity

As of 11 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2109.04450.

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

pith.paper-citation-record.v1
2109.04450 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 3 of 3 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:00:04.912493Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T16:20:03.873515Z

Reference resolution

0 of 0 outbound references displayed

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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 cb8616e1-e5e5-413a-a743-616dc6cd8753 · inbound

Strong gravitational lensing effects around rotating regular black holes cites this paper.

Strong gravitational lensing effects around rotating regular black holes Investigating strong gravitational lensing effects by suppermassive black holes with Horndeski gravity

Reference 50

Resolution
unresolved
no resolver link, observed 2026-08-10T23:00:04.912493Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 257efe16-2303-488b-95af-9b2ed0805a87 · inbound

Strong gravitational lensing by black hole in F(R) Euler Heisenberg Gravity's Rainbow cites this paper.

Strong gravitational lensing by black hole in F(R) Euler Heisenberg Gravity's Rainbow Investigating strong gravitational lensing effects by suppermassive black holes with Horndeski gravity

Reference 73

Resolution
verified exact
local_arxiv, observed 2026-08-06T16:20:03.984269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T16:19:56.127151Z digest=sha256:a23ae74fb6b4bcdeb1b5ea21ab39f578f6f46105f70e443fde69e332b590e038

Observation 8feed2d9-ac52-44bf-accd-05d78dfc0bf1 · inbound

Optical Landscapes and High-Energy Collisions in Hairy Horndeski Gravity cites this paper.

Optical Landscapes and High-Energy Collisions in Hairy Horndeski Gravity Investigating strong gravitational lensing effects by suppermassive black holes with Horndeski gravity

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-04T00:59:01.778734Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T00:59:01.778734Z digest=sha256:8359cd8e3a623ed837734437f8acd1b3a290ea840252a292537d8bb7db0a713a