Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-02T18:14:24.961793Z
Paper Citation Record · LEDGER
As of 23 August 2026, this Paper Citation Record lists 90 of 90 outbound references and 4 inbound Pith citation observations for arXiv:2603.17007.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-02T18:14:24.961793Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-15T14:41:29.923387Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-04T04:59:36.006374Z
90 of 90 outbound references displayed
External citation measurements
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Observation e70ddd62-3494-40e1-ae93-f8bcd055b77e · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Therefore, the norm of the four-momentum of photons with polarizationP + of the electromagnetic field is always null or spacelike with respect to the spacetime metric
Reference 1
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Unavailable: canonical work link unavailable.
Observation ffe64e47-217a-45f1-ab79-212cbce6ae1a · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Aaboudet al.[ATLAS Collaboration], Evidence for light- by-light scattering in heavy-ion collisions with the ATLAS de- tector at the LHC, Nature Phys.13, 852 (2017)
Reference 2
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Unavailable: canonical work link unavailable.
Observation dfefe2e4-f3dd-4a5d-b736-6b8316e965ab · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Aadet al.[ATLAS Collaboration], Observation of Light-by- Light Scattering in UltraperipheralP b+P bCollisions with the ATLAS Detector, Phys
Reference 3
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Unavailable: canonical work link unavailable.
Observation e26a59bf-89be-4162-8555-891b7c03ab5d · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Sirunyanet al.[CMS Collaboration], Evidence for light- by-light scattering and searches for axion-like particles in ultra- peripheralP bP bcollisions at√sN N= 5.02T eV, Phys
Reference 4
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Unavailable: canonical work link unavailable.
Observation 2c17af4a-8cdb-43e4-b1f3-21e75f3921eb · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 5
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Observation 172f8863-af0d-4749-b32f-72ffe73f3961 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 6
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Observation 7758d3ed-9bdc-47a6-89a9-7cb2dab14651 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Adamet al.[Star Collaboration], Measurement ofe +e− Momentum and Angular Distributions from Linearly Polarized Photon Collisions, Phys
Reference 7
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Unavailable: canonical work link unavailable.
Observation f61c1500-3fcd-4642-9edd-a94d3e8a48df · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Battestiet al., High magnetic fields for fundamental physics, Phys
Reference 8
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Unavailable: canonical work link unavailable.
Observation e5f872b8-ab9a-4c4f-b502-e8f2f63a27c2 · outbound
Reference 9
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Observation 88d8d381-63c2-4eb8-ab7e-4566248fc57a · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Euler and B
Reference 10
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Observation 535610f0-6699-4769-9fb9-3620bf331e9c · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Heisenberg and H
Reference 11
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Observation 99e6b963-f812-4261-a98d-5f98c1530911 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 12
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Observation 52854a1e-c5e8-4bef-b95f-9aa3080253e2 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 13
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Observation 7060b067-615c-4145-afcd-9b4562b35ab3 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Born-Infeld action, supersymmetry and string theory
Reference 14
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Unavailable: canonical work link unavailable.
Observation 718c438e-87cc-4f25-8b6d-950b925500d5 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Nonlinear Electrodynamics and QED
Reference 15
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Observation 9b0e6108-d659-4cd5-98fc-3d38e96c0e8e · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 16
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Observation dcd74343-1947-4392-a70a-f639937dcea9 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Regular black holes sourced by nonlinear electrodynamics
Reference 17
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Unavailable: canonical work link unavailable.
Observation 593a38e6-b6ec-4c36-ae21-0fa224c19597 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 18
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Observation 205a3455-65c4-4fc1-9b4d-8a27bb245c19 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Born, Modified Field Equations with a Finite Radius of the Electron, Nature132, 282 (1933)
Reference 19
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Observation 64affc2b-4b14-46c3-b896-66693b4ec598 · outbound
Reference 20
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Observation bf253aa5-41ae-44a4-95db-88c794992bd7 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Born, On the quantum theory of the electromagnetic field, Proc
Reference 21
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Unavailable: canonical work link unavailable.
Observation 237714a1-c27e-45e5-88f7-bada9c8bcb54 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Boillat, Nonlinear Electrodynamics: Lagrangians and Equa- tions of Motion, J
Reference 22
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Unavailable: canonical work link unavailable.
Observation 396516c5-01a3-4b27-813a-2b8c22aa6e47 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 23
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Observation 7218cf15-883a-49c6-b376-7e2e14700334 · outbound
Reference 24
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Observation e61489b0-c8f2-4a47-85a1-9659ddd8c08b · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Bambi,Regular Black Holes: Towards a New Paradigm of Gravitational Collapse, Springer Series in Astrophysics and Cosmology (Springer Singapore, 2023)
Reference 25
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Observation bb8beed8-784c-44c1-b145-8081f11ca86b · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Vrbaet al., Particle motion around generic black holes cou- pled to non-linear electrodynamics, Eur
Reference 26
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Unavailable: canonical work link unavailable.
Observation 310cac7f-6b27-459f-9d14-e75c709fb955 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 27
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Observation 65195783-7a44-4cb5-a2dd-de4e65507946 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Amaro and A
Reference 28
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Observation 1236e6d9-1886-4368-a6ca-5d362743a9f7 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Bound orbits around charged black holes with exponential and logarithmic electrodynamics
Reference 29
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Observation 22980b34-9b19-4604-9729-e13e1d3ad3e3 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Toshmatov, B
Reference 30
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Observation 68624e78-b34c-4845-b4d3-08704acca10d · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Breton and L
Reference 31
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Observation 0b27b1f0-9b71-4fe1-a2be-5c48ca379f00 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Stuchl ´ık and J
Reference 32
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Observation e806e86a-ec2a-4d58-b010-834a757843ce · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Stuchl ´ık, J
Reference 33
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Observation 94e518fd-04e0-4acb-b13d-d449b4f6e815 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Allahyari, M
Reference 34
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Observation 8a9a5027-cf33-4b75-a26b-9f7479bd51ca · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 35
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Observation 201973f3-c9b8-48c4-a179-5f8604aa73df · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Raymbaev, M
Reference 36
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Observation a01cc1a6-0afb-447f-9893-ff345625a719 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Huet al., QED effect on a black hole shadow, Phys
Reference 37
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Observation 9311d0d4-7973-4859-807f-03d68b5d6553 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 38
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Observation c43b60d8-ed1c-40b1-afcd-f7715d536b2b · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Liang, Strong gravitational lensing by regular electrically charged black holes, Gen
Reference 39
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Observation df202adb-e93a-424f-8162-43975e3396b4 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Liang, Regular Magnetic Black Hole Gravitational Lensing, Chinese Phys
Reference 40
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Observation 27e7b3aa-b35a-4931-b8ec-39efc3c88677 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Ghaffarnejad, M
Reference 41
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Observation 3b097a51-558f-45d9-8bb8-9c0870f065ec · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Schee and Z
Reference 42
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Observation 3c3a18da-54d5-4f4f-9d87-bf750941ab65 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 43
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Observation 1e87d2e6-c300-4ae1-9ccf-951bb7b3812f · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Tomizawa and R
Reference 44
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Observation 7be058f7-2926-467e-bfd9-2930f52acb55 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 45
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Observation 9399dd16-58a1-4a62-84a9-ad67bd344126 · outbound
Reference 46
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Observation 98e2b432-9390-482a-8e7a-a9c5ac0456bf · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 47
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Observation c88235e0-28c0-420d-9a7e-6c0f78d419c3 · outbound
Reference 48
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Observation e53a55a7-b31e-467b-82cc-db1137965a69 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Ay ´on-Beato and A
Reference 49
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Observation ea7ffad4-6598-4011-962b-b04d1c188dc7 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 50
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Observation c011bf30-31ef-4938-b9da-78b4afd2ab6e · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics D’Inverno and J
Reference 51
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Observation 5aac8b8b-2404-418e-b79d-ca7e3041c2cb · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Vagnozziet al., Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A∗, Class
Reference 52
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Observation 58671223-1135-4afb-9e82-6656dc954276 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 53
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Observation b5193796-7c35-4d96-a762-9ee43f14d1c9 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Greiner,Quantum Electrodynamics(Springer, Dordrecht, Netherlands, 2008)
Reference 54
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Observation edf7a638-f0ec-4449-96e5-e15a1f13d9a9 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Novello and E
Reference 55
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Observation 82645c97-f4cf-4da0-982f-fb5b8317efb1 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Wald,General Relativity(University of Chicago Press, Chicago, 1984)
Reference 56
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Reference 57
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Observation 4e6011cc-524b-41be-8fdc-4bfae5239120 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 58
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Observation 6508d0f6-1688-457d-b99f-18440b4bd69e · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 59
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Observation 2830a4d5-c364-41ef-8de2-b7c2f1f8d94c · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Nomura and D
Reference 60
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Observation 917e9739-37f6-4ed9-9380-31e83e4feaa5 · outbound
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Reference 61
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Observation 766a4482-de95-4f6c-bdf5-3b88ea037e45 · outbound
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Reference 62
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Observation 221ecb92-0166-497e-bf1e-901f4f62d8d9 · outbound
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Reference 63
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Observation 0e46263a-5d2c-4701-91c2-5d785af27f28 · outbound
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Reference 64
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Reference 65
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Observation fe4aebc8-4872-4ef5-8be8-0fe878482956 · outbound
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Reference 66
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Observation f8608d32-b026-4eaf-8206-52e9099db051 · outbound
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Reference 68
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Observation 35d969a8-8449-47c1-a378-631a9527d0ec · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 69
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Observation 17b7b0b3-ddd3-430c-b09d-3ea0532a0814 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Einstein, Lens-like action of a star by the deviation of light in the gravitational field, Science84, 506 (1936)
Reference 70
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Observation a109d2b3-e97e-4ec6-8f59-26446798a11e · outbound
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Reference 71
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Observation 269fef23-e910-4e44-97e4-54135d27ed41 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics ¨Ovg¨un, Weak field deflection angle by regular black holes with cosmic strings using the Gauss-Bonnet theorem, Phys
Reference 72
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Observation 3d3897ae-2ba5-47fd-bd7e-ff6ff269516b · outbound
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Observation a89e6c27-53e4-41cb-8611-909708128780 · outbound
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Observation 9f076151-faf8-4964-a417-da0748174602 · outbound
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Reference 75
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Observation 950719e9-7490-4c9d-b870-d73b04f1a709 · outbound
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Reference 76
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Observation 8805e101-31fc-4139-8e96-2dc63e4b97ce · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Ishihara, Y
Reference 77
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Observation 132b8224-ed26-4a6c-a44b-88e49f7c6bc5 · outbound
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Reference 78
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Observation 7bdbc21e-6b57-41e0-be52-43cb9bf017d5 · outbound
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Reference 79
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Observation 23bab97d-36c8-47c2-8ec6-51667145799f · outbound
Reference 80
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Observation 7f2bfa06-8790-46af-84bc-f58184e17d7a · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Arakida and M
Reference 81
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Reference 82
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Observation 4b2df6fa-9b6f-4aa7-987e-bb77bec9298e · outbound
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Reference 83
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Observation c6d60dac-5435-415f-8605-9e6eb6372730 · outbound
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Reference 84
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Observation 0962863e-5c69-4909-bb81-f3001110c532 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Unresolved cited work
Reference 85
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Observation 21ba24ee-06be-4a8b-880f-7525b9d13128 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Do et al., Relativistic redshift of the star S0-2 orbiting the Galactic Center supermassive black hole, Science365, 664 (2019)
Reference 86
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Observation 496a9dea-55f8-4b3d-9071-8ee5e633e979 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Abuteret al.[GRA VITY], Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole, Astron
Reference 87
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Observation 891956fe-db2c-4704-840e-57fd80b5ef6f · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Abuteret al.[GRA VITY], Polarimetry and astrometry of NIR flares as event horizon scale, dynamical probes for the mass of Sgr A⋆, Astron
Reference 88
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Observation 0447ac4c-fc47-4830-9add-671bae01c0db · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Zaja ˇcek, A
Reference 89
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Observation b9d3debf-3761-4c37-ba92-8fe22240ac87 · outbound
Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics Zaja ˇcek, A
Reference 90
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Observation 1c720ae5-6a2d-4682-87b3-ddc35be8996d · inbound
Constraining Black Hole Parameters in Non-Commutative Geometry using Machine Learning Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics
Reference 10
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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 449a7fd9-9259-462e-b73c-b6ac90609924 · inbound
Constitutive birefringence and critical curves in the rotating Garc\'ia--D\'iaz black hole Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 044f9fda-2fc2-430b-b6f9-f50ed54b7e24 · inbound
A causal magnetic black hole with finite self-energy Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics
Reference 73
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Observation aa1677c5-8502-43ea-8aab-ec078873aab2 · inbound
Probing nonlinear electrodynamics-sourced black holes via light and orbital mechanics Two shadows of a single black hole: Vacuum birefringence phenomena within Einstein-nonlinear-electrodynamics
Reference 49
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