Paper Citation Record · LEDGER

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods

As of 21 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2501.04509.

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

pith.paper-citation-record.v1
2501.04509 v2

Coverage vector

measured 33 of 33 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-10T21:38:36.525658Z

measured 33 of 33 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

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Pith citing papers itemized under the disclosed page cap.

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Reference resolution

33 of 33 outbound references displayed

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verified fuzzy25
unresolved7
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External citation measurements

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Outbound references

Observation b0bb3448-2102-459c-a6e1-a2d39964164b · outbound

This paper cites Abdujabbarov, F.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Abdujabbarov, F

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.857289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c5f96733-2115-45dd-81b0-af30383db226 · outbound

This paper cites an unresolved cited work.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:38:37.839428Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e2b25d8a-da77-4366-8246-d7784abc4559 · outbound

This paper cites Belinskii, V.E.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Belinskii, V.E

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.819613Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7f462582-6c36-4f88-9c54-e5eb56d0cd74 · outbound

This paper cites Belokolos, A.I.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Belokolos, A.I

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.800451Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d5445231-042f-47af-ac31-b76e6e3980ff · outbound

This paper cites an unresolved cited work.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:38:37.775069Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 81b8be44-cd52-4331-aede-0b17dd954ba7 · outbound

This paper cites Chandrasekharan.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Chandrasekharan

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.740085Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 800fb845-6f0e-47ea-a990-7d8f54de9854 · outbound

This paper cites https://doi.org/10.1007/s10714-018-2361-9.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods https://doi.org/10.1007/s10714-018-2361-9

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T21:38:36.065276Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 82b5add6-2618-436d-a91a-3ac9e1b733b5 · outbound

This paper cites de Leon, J.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods de Leon, J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.648891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 21c62259-8d5a-4175-9c15-36af2fc7d970 · outbound

This paper cites On a class of algebro-geometric solutions to the Ernst equation.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods On a class of algebro-geometric solutions to the Ernst equation

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-10T21:38:36.642881Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e6a3ed9a-073e-416d-97f0-ed38e91d4d4d · outbound

This paper cites Einstein, Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field, Science 84, 506 (1936).

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Einstein, Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field, Science 84, 506 (1936)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.627190Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2215dedf-7b4e-4986-b23e-bfb49d4df203 · outbound

This paper cites Ernst, New formulation of the axially symmetric gravitational field problem I , Phys.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Ernst, New formulation of the axially symmetric gravitational field problem I , Phys

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.594971Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b847b067-9c9d-49f1-b6c5-9ed8de55626c · outbound

This paper cites Ernst, New formulation of the axially symmetric gravitational field problem II , Phys.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Ernst, New formulation of the axially symmetric gravitational field problem II , Phys

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.569130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 027c641f-3642-4241-8cdb-6d0c2e3a07bf · outbound

This paper cites Frauendiener and C.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Frauendiener and C

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.545310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 650c59a0-e4df-4f20-9317-d30c983bb82a · outbound

This paper cites Grenzebach, V.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Grenzebach, V

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.520830Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3713890b-e362-4294-8bdc-096797761ecd · outbound

This paper cites Hackmann and C.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Hackmann and C

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.439918Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 91491952-bfae-4361-9b3d-f5721534a0b1 · outbound

This paper cites Klein, D.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Klein, D

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.352120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5cb62cf9-cd15-4e68-ad95-630970d899e0 · outbound

This paper cites Klein, O.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Klein, O

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.334921Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation dd8ca3f6-e94b-4016-a386-894f82a9a705 · outbound

This paper cites Klein and O.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Klein and O

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.310742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 25405398-0deb-47b3-a6c1-8564168a1a52 · outbound

This paper cites Korotkin.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Korotkin

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.293242Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 874cf1f8-ac23-4793-b6df-1fa61b1104c7 · outbound

This paper cites Korotkin, Solutions of the vacuum Einstein equation having toroidal infinite red-shift surface , Class.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Korotkin, Solutions of the vacuum Einstein equation having toroidal infinite red-shift surface , Class

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.272614Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 83d51c08-449a-4588-a890-c758b3b07a64 · outbound

This paper cites Korotkin, Algebraic Geometric Solutions of Einstein ’s Equations: Some Physical Properties , Commun.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Korotkin, Algebraic Geometric Solutions of Einstein ’s Equations: Some Physical Properties , Commun

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.159915Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e718b62e-d5f2-441c-a3fe-8b6b07841a40 · outbound

This paper cites Maison, Are the stationary axially symmetric Einstein equations completely integrable? Phys.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Maison, Are the stationary axially symmetric Einstein equations completely integrable? Phys

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.141007Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 663d54ab-cd15-45a5-8cbc-e3803a798f9c · outbound

This paper cites Manko and E.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Manko and E

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.116958Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f6b623ed-2d91-4ac1-b075-452186781128 · outbound

This paper cites Moreira, C.A.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Moreira, C.A

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.098218Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2ef77ffe-374c-4ff1-8aa4-cd7bd3a7e166 · outbound

This paper cites Neugebauer, Backlund transformations of axially symmetric stationary gravitational fields J.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Neugebauer, Backlund transformations of axially symmetric stationary gravitational fields J

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.073021Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 852d70ae-c86d-4b84-8380-56240ee217c1 · outbound

This paper cites Neugebauer, R.Meinel, General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions , Phys.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Neugebauer, R.Meinel, General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions , Phys

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.050456Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5d9e7ffd-d4bd-465d-a384-022c8553c77f · outbound

This paper cites Calculating black hole shadows: Review of analytical studies.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Calculating black hole shadows: Review of analytical studies

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-10T21:38:36.375679Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7d6c24d-aef8-4784-8939-aa59f6740e5c · outbound

This paper cites Silverman.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Silverman

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.030005Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2051999f-f527-456d-9a1e-18b56fa3361d · outbound

This paper cites Stephani, D.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Stephani, D

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:37.006807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4a7e12e5-9cbe-4012-9b0b-f5db1cdb1a29 · outbound

This paper cites an unresolved cited work.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:38:36.972862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 807a8567-ed08-4c73-9a31-1bb60f7674e9 · outbound

This paper cites Teo, Spherical Photon Orbits Around a Kerr Black Hole ,General Relativity and Gravitation.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Teo, Spherical Photon Orbits Around a Kerr Black Hole ,General Relativity and Gravitation

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:38:36.791323Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 16fb3ee0-2f78-454d-af05-d0aabd15654a · outbound

This paper cites an unresolved cited work.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:38:36.747328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9152719f-e2b9-4c8d-9f78-33b6e6c2e134 · outbound

This paper cites an unresolved cited work.

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:38:36.722652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.