Paper Citation Record · LEDGER

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity

As of 22 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2506.10414.

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

pith.paper-citation-record.v1
2506.10414 v3

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:34:55.318286Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

44 of 44 outbound references displayed

verified exact3
verified fuzzy14
unresolved27
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e11fbefd-9268-4191-968e-529ef1bcdfb1 · outbound

This paper cites First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:52.409843Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1368ec6a-3c33-4b36-a9f9-2f004e02e483 · outbound

This paper cites Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:52.471847Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc5a8c9d-e8de-40e9-8241-bc768d8f9c64 · outbound

This paper cites Angular radius of the black hole shadow for large distance ro >> mis αsh = 3 √ 3m ro.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Angular radius of the black hole shadow for large distance ro >> mis αsh = 3 √ 3m ro

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.354259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 67b1013d-9f6d-483e-afa6-81eaba24561c · outbound

This paper cites an unresolved cited work.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:52.525743Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 421f1981-80a4-4003-b1f5-aecf5e16a5cd · outbound

This paper cites The Cosmological Constant Problem and Quintessence.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity The Cosmological Constant Problem and Quintessence

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:52.614058Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d8cc348-ffc3-4593-a748-33711c0b4841 · outbound

This paper cites The Case for a Positive Cosmological Lambda-term.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity The Case for a Positive Cosmological Lambda-term

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:52.675503Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2fbc8ac-8907-4674-9f26-2427f30950a7 · outbound

This paper cites A new recipe for $\Lambda$CDM.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity A new recipe for $\Lambda$CDM

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:34:56.003960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a265f7aa-3d59-4a2a-a8d0-b0372f9eec23 · outbound

This paper cites Particle Dark Matter: Evidence, Candidates and Constraints.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Particle Dark Matter: Evidence, Candidates and Constraints

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:52.781986Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18f8379f-265c-4cf0-b300-0f38e254b117 · outbound

This paper cites How Cold is Cold Dark Matter?.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity How Cold is Cold Dark Matter?

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:52.845116Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3589571f-8643-4a7d-b1a0-198c8a981b84 · outbound

This paper cites Dark Matter properties through cosmic history.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Dark Matter properties through cosmic history

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:52.924845Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 04b6077a-7c74-424a-90d3-484c84737095 · outbound

This paper cites Challenges for $\Lambda$CDM: An update.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Challenges for $\Lambda$CDM: An update

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:53.000766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac525a89-d168-4485-a225-af56e6e8880a · outbound

This paper cites Probing the cold nature of dark matter.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Probing the cold nature of dark matter

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:53.056297Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34b51e92-d9f3-466f-b4cc-bd1a6370c581 · outbound

This paper cites Effect of the modified gravity on the large scale structure formation.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Effect of the modified gravity on the large scale structure formation

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:34:55.768190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 26d39d7b-e931-42a1-96c4-559508c0c44a · outbound

This paper cites Dark matter as scalaron in $f(R)$ gravity models.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Dark matter as scalaron in $f(R)$ gravity models

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:53.291438Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07c1f07c-7ce3-4085-adbe-3a60215cf2a6 · outbound

This paper cites Light deflection angle through velocity profile of galaxies in $f(R)$ model.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Light deflection angle through velocity profile of galaxies in $f(R)$ model

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:53.410015Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 359d0f07-a838-4493-b107-fffcbe92267b · outbound

This paper cites Snepppen, Scientific reports 11, 14247 (2021).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Snepppen, Scientific reports 11, 14247 (2021)

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.334886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 575b4d84-6e11-439c-90a5-c5b02d50aa4e · outbound

This paper cites Akiyama, A.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Akiyama, A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.326004Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c22b9afb-c42e-4786-a50d-1e143634b5b9 · outbound

This paper cites Synge, Monthly Notices of the Royal Astronomical So- ciety 131, 463 (1966).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Synge, Monthly Notices of the Royal Astronomical So- ciety 131, 463 (1966)

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.316894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 35222921-69af-4e5b-8d6e-0efb56b4b75f · outbound

This paper cites Perlick and O.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Perlick and O

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.307204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5ea8bf3e-24fc-42d0-8b06-b580c62da460 · outbound

This paper cites Takahashi, The Astrophysical Journal 611, 996 (2004).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Takahashi, The Astrophysical Journal 611, 996 (2004)

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.298776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 39210105-d3fa-4ce1-b3d2-f425201f6aff · outbound

This paper cites an unresolved cited work.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:34:56.290073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e3473af7-b4ab-48eb-8597-310d3e832e81 · outbound

This paper cites an unresolved cited work.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:34:56.281028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ff31acb2-4a03-494e-8717-1b98f244950a · outbound

This paper cites an unresolved cited work.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:34:56.272104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5a16827e-50ba-4322-bcc3-45ec7bf4d526 · outbound

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

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:54.035667Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9380b9e-eb83-48ef-b7f5-46073c726369 · outbound

This paper cites Schwarzschild, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften , 189 (1916).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Schwarzschild, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften , 189 (1916)

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:54.087119Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 314cdffe-e841-4807-bef9-f864c33822ad · outbound

This paper cites an unresolved cited work.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:34:56.256569Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 182e288e-16b8-47cd-8193-11b8aac4a9c4 · outbound

This paper cites Schutz, A first course in general relativity (Cambridge university press, 2022).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Schutz, A first course in general relativity (Cambridge university press, 2022)

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.247299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dcb7e9a3-67b5-4dc1-978d-b11c3be76b18 · outbound

This paper cites Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley and Sons, New York, 1972).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley and Sons, New York, 1972)

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:54.251778Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2bbc5e82-89aa-457d-92db-186d468c03e1 · outbound

This paper cites Sitzungs- berichte der k ˜A¶niglich preussischen akademie der wissenschaften zu berlin,.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Sitzungs- berichte der k ˜A¶niglich preussischen akademie der wissenschaften zu berlin,

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.231480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2cce0aff-4ffa-4de1-b752-440ebfc4ab83 · outbound

This paper cites The shadows and observational appearance of a noncommutative black hole surrounded by various profiles of accretions.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity The shadows and observational appearance of a noncommutative black hole surrounded by various profiles of accretions

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:54.377867Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ca8195c-9011-40d5-956d-6b92462494ba · outbound

This paper cites Chaotic Shadows of Black Holes: A Short Review.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Chaotic Shadows of Black Holes: A Short Review

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:54.434626Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f26b6f2e-6044-425d-aaa6-b24fb5762b72 · outbound

This paper cites Kottler, Annalen der Physik 361, 401 (1918).

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Kottler, Annalen der Physik 361, 401 (1918)

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.221525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c85ea5cd-9680-498a-8ec0-e17de31ca09a · outbound

This paper cites an unresolved cited work.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:54.526579Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 499dd908-2907-4469-833c-25013674b024 · outbound

This paper cites an unresolved cited work.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:54.581214Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0dce7c22-b2e3-4d35-a894-5d76fedeb834 · outbound

This paper cites an unresolved cited work.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:54.667288Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5163c7c5-fb05-490c-abe5-c968d72b678d · outbound

This paper cites Photon Rings around Kerr and Kerr-like Black Holes.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Photon Rings around Kerr and Kerr-like Black Holes

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:54.673593Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79029adf-21cf-4ad9-83c0-bc0b5412525a · outbound

This paper cites an unresolved cited work.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:34:56.344987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8f1f76e4-bf4c-4172-b915-4b56f83d4473 · outbound

This paper cites Extended galactic rotational velocity profiles in $f(R)$ gravity background.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Extended galactic rotational velocity profiles in $f(R)$ gravity background

Reference 41

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:34:55.551610Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation da3a0c3c-0f0a-442f-94b3-de3540df3da8 · outbound

This paper cites Unified $f(R)$ gravity at local scales.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Unified $f(R)$ gravity at local scales

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-07T04:34:54.986937Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23482edd-df5f-4363-837d-0c38a293e884 · outbound

This paper cites Nojiri and S.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Nojiri and S

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.193059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6256523f-492a-48f9-adca-1711732ed216 · outbound

This paper cites Nojiri and S.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Nojiri and S

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.184082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0892b76b-57b3-41e6-a319-da5949c7e277 · outbound

This paper cites Capozziello, K.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Capozziello, K

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.174820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ec47ff00-de1f-45b9-a921-5adc24053a3d · outbound

This paper cites De Felice and S.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity De Felice and S

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.165687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation fa73745a-62ea-406c-ad74-55c9ae03d357 · outbound

This paper cites Nojiri, S.

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity Nojiri, S

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:34:56.155012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.