{"as_of":"2026-08-18T05:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c687fe22088eca3a559eeba7e8e2e72450daa5df539783b8380abf1b01b3832d","coverage":[{"denominator":85,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":85,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T16:40:23.380584Z","state":"measured"},{"denominator":87,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":87,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-16T15:42:53.936778Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-16T15:43:03.575821Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"cited_work":{"arxiv_id":"2507.13048","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.13048","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"9e338d51-70c7-4bd6-a0c0-cc58b88b9541","year":2025},"citing_paper":{"arxiv_id":"2601.06864","last_updated":"2026-05-05T01:33:32Z","snapshot_observed_at":"2026-08-17T01:46:33.234658Z","submitted_at":"2026-01-11T11:17:16Z","title":"Boundary-only weak deflection angles from isothermal optical geometry","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-05-16T15:42:53.936778Z"},"links":{"cited_paper":"/paper/2507.13048","citing_paper":"/paper/2601.06864"},"observation_digest":"sha256:845a714a2bf84c738615d6256d478bf67a59d5a5695c8de8a1db5ec36dbd0b8b","observation_id":"ca50d4ce-52d1-4587-a019-eac1cb0d1c78","resolution":{"observed_at":"2026-05-16T15:43:03.577385Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"cited_work":{"arxiv_id":"2507.13048","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.13048","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"9e338d51-70c7-4bd6-a0c0-cc58b88b9541","year":2025},"citing_paper":{"arxiv_id":"2604.13564","last_updated":"2026-04-15T07:21:33Z","snapshot_observed_at":"2026-08-11T09:03:17.518041Z","submitted_at":"2026-04-15T07:21:33Z","title":"Topologically equivalent yet radiatively distinct orbits in EMRI system","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-10T13:04:39.993350Z"},"links":{"cited_paper":"/paper/2507.13048","citing_paper":"/paper/2604.13564"},"observation_digest":"sha256:44e9374481b7a14b2ad2677248f0926f3aba424c1faff5084c2c509c49986700","observation_id":"64841d92-be63-4c20-b033-826f4f3fd377","resolution":{"observed_at":"2026-05-10T13:05:24.530604Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.13048/citation-record","integrity":"/paper/2507.13048/integrity","json":"/paper/2507.13048/citation-record.json","paper":"/paper/2507.13048"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:15.287985Z","title":null,"venue":null,"work_id":null,"year":1920},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:15.287985Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:0de9bc34483719775061b991f7cab8b734e0dba3f78dc7df22aab8526a494001","observation_id":"9d191113-b133-4b7f-8874-d43ce5598e34","resolution":{"observed_at":"2026-08-06T16:40:15.287985Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:15.359128Z","title":"Einstein, Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field, Science 84, 506-507 (1936) doi:10.1126/science.84.2188.506 16","venue":null,"work_id":null,"year":1936},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:15.359128Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:ec270b5daa6b51a4ac8b34481cad5e8051184f78498f707539774b913b76ad54","observation_id":"237c0be7-26a4-409a-ac05-4ed5e00331f8","resolution":{"observed_at":"2026-08-06T16:40:15.359128Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:15.442859Z","title":null,"venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:15.442859Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:a4e12b41cc153a684f114e45339a8ee81b7f5a9ec9e4c1d35ad8f2969cf1e82d","observation_id":"f27901e9-3420-47e6-8c49-bff89b451247","resolution":{"observed_at":"2026-08-06T16:40:15.442859Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"astro-ph/9812172","last_updated":"1998-12-09T09:52:49Z","snapshot_observed_at":"2026-08-15T16:02:08.292448Z","submitted_at":"1998-12-09T09:52:49Z","title":"Probing the Universe with Weak Lensing","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"astro-ph/9812172","snapshot_observed_at":"2026-08-06T16:40:15.544584Z","title":"Mellier, Probing the universe with weak lensing, Ann","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:15.544584Z"},"links":{"cited_paper":"/paper/astro-ph/9812172","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:cb447a07983942757d7ad6cf97e5c3064a5aa864e614957ed37d5775541ecbeb","observation_id":"ef3a9348-2ab2-4545-b665-be36646731f5","resolution":{"observed_at":"2026-08-06T16:40:15.544584Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"astro-ph/9912508","last_updated":"1999-12-23T23:20:38Z","snapshot_observed_at":"2026-08-11T07:37:11.436931Z","submitted_at":"1999-12-23T23:20:38Z","title":"Weak Gravitational Lensing","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"astro-ph/9912508","snapshot_observed_at":"2026-08-06T16:40:15.623133Z","title":"Bartelmann and P","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:15.623133Z"},"links":{"cited_paper":"/paper/astro-ph/9912508","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:c3de6dd6f7f1a924f9fcddf17708674c51dbc74de1d3b32fc4471f9b5052da21","observation_id":"39979372-1be3-4ff1-aec0-5ef6426e5ad2","resolution":{"observed_at":"2026-08-06T16:40:15.623133Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1303.1808","last_updated":"2013-03-07T20:42:16Z","snapshot_observed_at":"2026-08-15T00:26:11.778691Z","submitted_at":"2013-03-07T20:42:16Z","title":"CFHTLenS tomographic weak lensing cosmological parameter constraints: Mitigating the impact of intrinsic galaxy alignments","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1303.1808","snapshot_observed_at":"2026-08-06T16:40:15.714716Z","title":"Heymans, E","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:15.714716Z"},"links":{"cited_paper":"/paper/1303.1808","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:34ca734bb550d79ef10bb9c606f81332912c401f610c9cdfe95564924d1243e9","observation_id":"f5bafc29-96b1-4a7a-bdcd-9a5a2bf15615","resolution":{"observed_at":"2026-08-06T16:40:15.714716Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:15.790492Z","title":"Kaiser and G","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:15.790492Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:e6c79ae1742aded4ebbcdb32d8e15d160aa8b15909a3b81272fdd49fd61dab77","observation_id":"97001b97-367c-4c76-ad5b-0bc53a20923a","resolution":{"observed_at":"2026-08-06T16:40:15.790492Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"astro-ph/0608407","last_updated":"2006-08-19T17:51:03Z","snapshot_observed_at":"2026-08-15T11:05:40.330161Z","submitted_at":"2006-08-19T17:51:03Z","title":"A direct empirical proof of the existence of dark matter","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"astro-ph/0608407","snapshot_observed_at":"2026-08-06T16:40:15.869242Z","title":"Clowe, M","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:15.869242Z"},"links":{"cited_paper":"/paper/astro-ph/0608407","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:6c2f056144547660c3f534759fe116960ba677a743cad518e9ba89c58bcf0860","observation_id":"a4be3057-f3c8-4955-9a11-dc398e142be6","resolution":{"observed_at":"2026-08-06T16:40:15.869242Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:15.979435Z","title":"Atamurotov, A","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:15.979435Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:34ea60ab92115bc794faaebce1378acd1e6f820a158ecbc44f898285016b6350","observation_id":"c4166070-9bc5-4a65-b3a5-38164963a088","resolution":{"observed_at":"2026-08-06T16:40:15.979435Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physrevd.73.023006","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Biesiada, Strong lensing systems as a probe of dark energy in the universe, Phys","venue":"Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology","work_id":"1c205163-1562-45f0-8b7e-9834826ff63e","year":2006},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:16.055240Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:bd677f02be11bd6a5360ac8a3fa01f066ad38e554cdc09b2baac0bf8e3265fa0","observation_id":"149a45ee-ce0e-4a6a-9b2f-131a76bd3a88","resolution":{"observed_at":"2026-08-06T16:40:23.541883Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1509.07649","last_updated":"2015-09-25T09:30:35Z","snapshot_observed_at":"2026-08-14T22:30:52.274436Z","submitted_at":"2015-09-25T09:30:35Z","title":"Cosmology with Strong Lensing Systems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1509.07649","snapshot_observed_at":"2026-08-06T16:40:16.135323Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:16.135323Z"},"links":{"cited_paper":"/paper/1509.07649","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:b9f1927924b9edab1c0d77fe07d76f35ce63036db29fe9f0c786e0d27c840fb6","observation_id":"ed8053a4-f920-4441-a6b5-46abe8419f53","resolution":{"observed_at":"2026-08-06T16:40:16.135323Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2002.11124","last_updated":"2020-02-25T19:00:01Z","snapshot_observed_at":"2026-07-06T09:00:07.035049Z","submitted_at":"2020-02-25T19:00:01Z","title":"Dark Energy Survey Year 1 Results: Cosmological Constraints from Cluster Abundances and Weak Lensing","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.11124","snapshot_observed_at":"2026-08-06T16:40:16.252180Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:16.252180Z"},"links":{"cited_paper":"/paper/2002.11124","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:c068227ce633823e9833fca282acc435c13818d738a02eaf4df4d9bef10c835e","observation_id":"b7ee6954-6dd7-41a9-94de-f1a69f67f017","resolution":{"observed_at":"2026-08-06T16:40:16.252180Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.13549","last_updated":"2022-03-21T13:57:33Z","snapshot_observed_at":"2026-08-14T23:39:27.638377Z","submitted_at":"2021-05-28T01:58:58Z","title":"Dark Energy Survey Year 3 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.13549","snapshot_observed_at":"2026-08-06T16:40:16.410649Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:16.410649Z"},"links":{"cited_paper":"/paper/2105.13549","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:cd622d0af97b2d6383c2ef5a2fd7f17201354b55ad1312f3816cc4a2f17aad6c","observation_id":"081436f5-5c62-4eba-8cde-78b7a8503b37","resolution":{"observed_at":"2026-08-06T16:40:16.410649Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2112.04149","last_updated":"2021-12-08T07:34:28Z","snapshot_observed_at":"2026-08-16T17:36:16.393689Z","submitted_at":"2021-12-08T07:34:28Z","title":"Geometrization of light bending and its application to SdSw spacetime","version":1},"cited_work":{"arxiv_id":"2112.04149","doi":null,"metadata_source":"pith","pith_arxiv_id":"2112.04149","snapshot_observed_at":"2026-08-06T16:40:26.559604Z","title":"Geometrization of light bending and its application to SdSw spacetime","venue":"gr-qc","work_id":"6d4e0897-2763-46d7-8585-908c1d99302a","year":2021},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:16.579253Z"},"links":{"cited_paper":"/paper/2112.04149","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:73af8741261e2469999ce0457a68b95a9b1f34d0427ade602ca7a64588f7d8e7","observation_id":"948c22cf-3675-46fb-b63b-491733c515ed","resolution":{"observed_at":"2026-08-06T16:40:26.645439Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"astro-ph/0005414","last_updated":"2000-05-19T22:01:33Z","snapshot_observed_at":"2026-08-12T19:16:08.917765Z","submitted_at":"2000-05-19T22:01:33Z","title":"The Discovery of a Luminous z=5.80 Quasar from the Sloan Digital Sky Survey","version":1},"cited_work":{"arxiv_id":"astro-ph/0005414","doi":null,"metadata_source":"pith","pith_arxiv_id":"astro-ph/0005414","snapshot_observed_at":"2026-08-06T16:40:26.396474Z","title":"The Discovery of a Luminous z=5.80 Quasar from the Sloan Digital Sky Survey","venue":"astro-ph","work_id":"dc53472a-dd4e-46e3-88be-dbc1b55352d5","year":2000},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:16.732539Z"},"links":{"cited_paper":"/paper/astro-ph/0005414","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:5c9da99d92d434618639c9b01b3c86c66aff336d9a9a119b2c117cb33e793a5e","observation_id":"7e81f3d5-bd3c-4938-8b7a-892c094ecaf4","resolution":{"observed_at":"2026-08-06T16:40:26.465972Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"astro-ph/0603248","last_updated":"2006-05-27T12:52:39Z","snapshot_observed_at":"2026-08-07T14:07:30.355983Z","submitted_at":"2006-03-09T20:37:52Z","title":"Probing the Coevolution of Supermassive Black Holes and Galaxies Using Gravitationally Lensed Quasar Hosts","version":3},"cited_work":{"arxiv_id":"astro-ph/0603248","doi":null,"metadata_source":"pith","pith_arxiv_id":"astro-ph/0603248","snapshot_observed_at":"2026-08-06T16:40:26.230936Z","title":"Probing the Coevolution of Supermassive Black Holes and Galaxies Using Gravitationally Lensed Quasar Hosts","venue":"astro-ph","work_id":"8a26efc2-4436-4d92-84b5-810382321376","year":2006},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:16.804723Z"},"links":{"cited_paper":"/paper/astro-ph/0603248","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:751a9ff28fa758880262b44e08705fdd94e312e65d6b48035f410bd272b73281","observation_id":"4a669bf1-78fb-4c19-8f98-42f279166f2f","resolution":{"observed_at":"2026-08-06T16:40:26.308360Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:16.918750Z","title":"Oguri and P","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:16.918750Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:5e82e1d76fc74c4bbe1a49e862b38697c089333c1a3032c81a13360bd443e4ac","observation_id":"4a3b94ac-e668-4b84-89c8-859c2bb6dec8","resolution":{"observed_at":"2026-08-06T16:40:16.918750Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2112.02821","last_updated":"2021-12-06T07:18:43Z","snapshot_observed_at":"2026-08-16T17:36:51.094559Z","submitted_at":"2021-12-06T07:18:43Z","title":"Revisiting the Lensed Fraction of High-Redshift Quasars","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2112.02821","snapshot_observed_at":"2026-08-06T16:40:17.016322Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:17.016322Z"},"links":{"cited_paper":"/paper/2112.02821","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:2d370adf9086d5960f79cf03e18d395aeb8b5dc0968408f6c9521eb66b606b20","observation_id":"6ea8ca06-bd83-4567-9edb-34d94d755f4d","resolution":{"observed_at":"2026-08-06T16:40:17.016322Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"ph/0310163","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:26.016947Z","title":"Seljak and C","venue":null,"work_id":"204479f6-54fb-4b57-bfb1-cff4eb48e943","year":2004},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:17.084115Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:bea5ec53d9ef842a30eb2d1f4a5c3b1d519c87bc8deb424e1c2e372f29309cab","observation_id":"2743fc8e-588a-42de-add7-95f285df02b9","resolution":{"observed_at":"2026-08-06T16:40:26.071432Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2106.06545","last_updated":"2021-11-02T09:20:38Z","snapshot_observed_at":"2026-08-16T18:17:43.951652Z","submitted_at":"2021-06-11T18:00:01Z","title":"Evidence for lensing of gravitational waves from LIGO-Virgo","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.06545","snapshot_observed_at":"2026-08-06T16:40:17.219347Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:17.219347Z"},"links":{"cited_paper":"/paper/2106.06545","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:061c956c99a0bb13a9b0060687ec9e1da104ad0658d3f2cf2dc612b5e61b9bfe","observation_id":"ec916cda-b50e-4ad7-88fe-4ccf2f0b166c","resolution":{"observed_at":"2026-08-06T16:40:17.219347Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2107.05046","last_updated":"2021-07-11T13:39:05Z","snapshot_observed_at":"2026-08-17T01:03:47.096978Z","submitted_at":"2021-07-11T13:39:05Z","title":"Probing modified gravitational wave propagation with strongly lensed coalescing binaries","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2107.05046","snapshot_observed_at":"2026-08-06T16:40:17.361464Z","title":"Finke, S","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:17.361464Z"},"links":{"cited_paper":"/paper/2107.05046","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:91296259539c3af5dd505797aeeca243fb15db2ce09767d58edb6ee84a69b044","observation_id":"4a8c0414-e4ff-40de-a5a7-e6d942015aed","resolution":{"observed_at":"2026-08-06T16:40:17.361464Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0805.4812","last_updated":"2008-07-14T17:18:07Z","snapshot_observed_at":"2026-08-15T10:14:18.233132Z","submitted_at":"2008-05-30T19:02:44Z","title":"Weak Lensing Probes of Modified Gravity","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0805.4812","snapshot_observed_at":"2026-08-06T16:40:17.478394Z","title":"Schmidt, Weak Lensing Probes of Modified Gravity, Phys","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:17.478394Z"},"links":{"cited_paper":"/paper/0805.4812","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:7d74ea5314cfa821d19f3c46cc8089d4460eddc8305ceff6b89f0b29b2ccaa87","observation_id":"26303b63-8ad0-4544-b3ef-f56180653fab","resolution":{"observed_at":"2026-08-06T16:40:17.478394Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0906.2221","last_updated":"2009-06-12T19:08:16Z","snapshot_observed_at":"2026-08-16T15:20:23.712329Z","submitted_at":"2009-06-12T19:08:16Z","title":"Tests of Gravity from Imaging and Spectroscopic Surveys","version":1},"cited_work":{"arxiv_id":"0906.2221","doi":null,"metadata_source":"pith","pith_arxiv_id":"0906.2221","snapshot_observed_at":"2026-08-06T16:40:25.751052Z","title":"Tests of Gravity from Imaging and Spectroscopic Surveys","venue":"astro-ph.CO","work_id":"86106e6e-851d-463e-ad00-3b3f13d725fc","year":2009},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:17.620735Z"},"links":{"cited_paper":"/paper/0906.2221","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:7eca302a154231527ca45374cb898120dd382fcc33a78d875741778e58a734ca","observation_id":"3e547f45-3853-4002-b41a-ddb9779ee2a6","resolution":{"observed_at":"2026-08-06T16:40:25.831689Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1511.01318","last_updated":"2016-05-13T00:38:29Z","snapshot_observed_at":"2026-08-14T22:24:53.280850Z","submitted_at":"2015-11-04T13:03:33Z","title":"The Distance Duality Relation from Strong Gravitational Lensing","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1511.01318","snapshot_observed_at":"2026-08-06T16:40:17.736000Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:17.736000Z"},"links":{"cited_paper":"/paper/1511.01318","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:4f7d7d43430b484ba87381f754a89684bd261d153a9846c5581aa0de7282bac3","observation_id":"de5a77b1-7bde-47d4-9c47-68e1d2bf1cf2","resolution":{"observed_at":"2026-08-06T16:40:17.736000Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1708.00935","last_updated":"2017-12-06T13:34:56Z","snapshot_observed_at":"2026-08-14T20:43:33.980829Z","submitted_at":"2017-08-02T21:21:47Z","title":"Phantom wormholes in Einstein-Maxwell-dilaton theory","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1708.00935","snapshot_observed_at":"2026-08-06T16:40:17.831439Z","title":"Goulart, Phantom wormholes in Einstein–Maxwell-dilaton theory, Class","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:17.831439Z"},"links":{"cited_paper":"/paper/1708.00935","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:5ac99f4cd282b266da39d5462d9391be86211972ecbcaab1e36090383cd0b55f","observation_id":"85a4647a-44bb-4268-8281-a0d8e5d3c0ed","resolution":{"observed_at":"2026-08-06T16:40:17.831439Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2005.13096","last_updated":"2020-07-25T22:52:04Z","snapshot_observed_at":"2026-08-03T03:43:27.663101Z","submitted_at":"2020-05-27T00:23:29Z","title":"Gravitational lensing in a black-bounce traversable wormhole spacetime","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2005.13096","snapshot_observed_at":"2026-08-06T16:40:17.969889Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:17.969889Z"},"links":{"cited_paper":"/paper/2005.13096","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:c00378c55ab813232014531542cdc0feb64de35ec00492d53e00efa5498875d3","observation_id":"46d994d7-a5e6-490e-b822-0e69f8508403","resolution":{"observed_at":"2026-08-06T16:40:17.969889Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2112.10802","last_updated":"2021-12-20T19:01:16Z","snapshot_observed_at":"2026-08-16T17:33:10.466630Z","submitted_at":"2021-12-20T19:01:16Z","title":"Einstein-Maxwell-dilaton neutral black holes in strong magnetic fields: topological charge, shadows and lensing","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2112.10802","snapshot_observed_at":"2026-08-06T16:40:18.091355Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:18.091355Z"},"links":{"cited_paper":"/paper/2112.10802","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:2eb62c709e9d5d24363dce7a058da6ef2bc866bb7cc90478f3c3d3993af29dd5","observation_id":"53766b38-b485-4de5-b253-8e28dbae6f94","resolution":{"observed_at":"2026-08-06T16:40:18.091355Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2104.00696","last_updated":"2021-09-07T17:00:56Z","snapshot_observed_at":"2026-08-16T18:34:24.387387Z","submitted_at":"2021-04-01T18:03:47Z","title":"Strong gravitational lensing by rotating Simpson--Visser black holes","version":3},"cited_work":{"arxiv_id":"2104.00696","doi":null,"metadata_source":"pith","pith_arxiv_id":"2104.00696","snapshot_observed_at":"2026-08-06T16:40:25.572861Z","title":"Strong gravitational lensing by rotating Simpson--Visser black holes","venue":"gr-qc","work_id":"92e6d384-450d-49eb-9bd6-6fa60154d26b","year":2021},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:18.225985Z"},"links":{"cited_paper":"/paper/2104.00696","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:961f1c2a2308ad6f132c151a8093822a977b95430cf3b8ee1b82fc34afdd4154","observation_id":"eab84588-ffc7-41c4-a225-fffa91dc09a8","resolution":{"observed_at":"2026-08-06T16:40:25.641548Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2202.09641","last_updated":"2022-04-21T00:37:33Z","snapshot_observed_at":"2026-08-16T17:20:06.530643Z","submitted_at":"2022-02-19T16:58:07Z","title":"Retrolensing by two photon spheres of a black-bounce spacetime","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2202.09641","snapshot_observed_at":"2026-08-06T16:40:18.317170Z","title":"Tsukamoto, Retrolensing by two photon spheres of a black-bounce spacetime, Phys","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:18.317170Z"},"links":{"cited_paper":"/paper/2202.09641","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:da2401e6c65aa33fe82e3ceb39930914cde2fe06f39c417061238d3fb226d2ce","observation_id":"aff4af90-a4e6-4243-986f-7c24dc590d64","resolution":{"observed_at":"2026-08-06T16:40:18.317170Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.11238","last_updated":"2019-06-26T18:06:46Z","snapshot_observed_at":"2026-08-13T13:53:05.353909Z","submitted_at":"2019-06-26T18:06:46Z","title":"First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.11238","snapshot_observed_at":"2026-08-06T16:40:18.436817Z","title":"Akiyama et al","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:18.436817Z"},"links":{"cited_paper":"/paper/1906.11238","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:fe89a1f578e150ebd769cf6c7c9be2a8bd313fac9bb941d913680e237c480468","observation_id":"e09fc92e-6bd0-4465-9f5a-5181e6ef4a14","resolution":{"observed_at":"2026-08-06T16:40:18.436817Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.11239","last_updated":"2019-06-26T18:06:47Z","snapshot_observed_at":"2026-08-13T20:35:04.499769Z","submitted_at":"2019-06-26T18:06:47Z","title":"First M87 Event Horizon Telescope Results. II. Array and Instrumentation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.11239","snapshot_observed_at":"2026-08-06T16:40:18.520981Z","title":"Akiyama et al","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:18.520981Z"},"links":{"cited_paper":"/paper/1906.11239","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:d5a617d953cc50f6f749486424ab8d1361c76e78e5b5e1c9f8fbad97d281fab5","observation_id":"deeb004d-6d47-40de-9f0d-14c86a1a6d8a","resolution":{"observed_at":"2026-08-06T16:40:18.520981Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.11240","last_updated":"2019-06-26T18:06:48Z","snapshot_observed_at":"2026-08-16T22:06:41.334535Z","submitted_at":"2019-06-26T18:06:48Z","title":"First M87 Event Horizon Telescope Results. III. Data Processing and Calibration","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.11240","snapshot_observed_at":"2026-08-06T16:40:18.584002Z","title":"Akiyama et al.[Event Horizon Telescope], First M87 Event Horizon Telescope Results","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:18.584002Z"},"links":{"cited_paper":"/paper/1906.11240","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:be499cba7b3240d1e0e6a17133510a0b927955ddfa7b85e4fb018e94e40f3765","observation_id":"370660b6-6d7f-441b-b00e-757b4a0a9586","resolution":{"observed_at":"2026-08-06T16:40:18.584002Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.11241","last_updated":"2019-06-26T18:06:49Z","snapshot_observed_at":"2026-08-12T15:02:17.279934Z","submitted_at":"2019-06-26T18:06:49Z","title":"First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.11241","snapshot_observed_at":"2026-08-06T16:40:18.654269Z","title":"Akiyama et al","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:18.654269Z"},"links":{"cited_paper":"/paper/1906.11241","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:3d43c61e4116f418946ead699e37fa77e66ad43e1e3de3088e9fc2440a92428c","observation_id":"b3224560-23ff-4b27-b953-bb6b126590be","resolution":{"observed_at":"2026-08-06T16:40:18.654269Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.11242","last_updated":"2019-06-26T18:06:50Z","snapshot_observed_at":"2026-07-06T08:03:03.170900Z","submitted_at":"2019-06-26T18:06:50Z","title":"First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.11242","snapshot_observed_at":"2026-08-06T16:40:18.777799Z","title":"Akiyama et al","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:18.777799Z"},"links":{"cited_paper":"/paper/1906.11242","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:a48b47fb5e0746114b1ce44f5e618059f4fa777cc7ebd616853dd570a78f586d","observation_id":"eb2f9c08-2ee0-4a50-a519-f7eaa82f1d5f","resolution":{"observed_at":"2026-08-06T16:40:18.777799Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.11243","last_updated":"2019-06-26T18:06:51Z","snapshot_observed_at":"2026-07-06T08:03:03.170900Z","submitted_at":"2019-06-26T18:06:51Z","title":"First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.11243","snapshot_observed_at":"2026-08-06T16:40:18.885480Z","title":"Akiyama et al.[Event Horizon Telescope], First M87 Event Horizon Telescope Results","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:18.885480Z"},"links":{"cited_paper":"/paper/1906.11243","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:fd6e08849156467a351ae1a8a3a1097bcfd01691d8f6e84f175af8ff66acc1be","observation_id":"0022fdf1-a68e-486c-9bf6-50a9c085b855","resolution":{"observed_at":"2026-08-06T16:40:18.885480Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.01169","last_updated":"2021-05-03T21:12:04Z","snapshot_observed_at":"2026-08-16T18:27:17.379388Z","submitted_at":"2021-05-03T21:12:04Z","title":"First M87 Event Horizon Telescope Results. VII. Polarization of the Ring","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.01169","snapshot_observed_at":"2026-08-06T16:40:18.974406Z","title":"Akiyama et al","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:18.974406Z"},"links":{"cited_paper":"/paper/2105.01169","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:270ef6b71b0a864917a834676fff37b6b458c8d363944fa7a3ee6257681e40d5","observation_id":"27c8a733-fe55-4633-b402-3af0e531d0e4","resolution":{"observed_at":"2026-08-06T16:40:18.974406Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.01173","last_updated":"2021-05-05T12:39:47Z","snapshot_observed_at":"2026-08-18T01:11:42.716210Z","submitted_at":"2021-05-03T21:22:13Z","title":"First M87 Event Horizon Telescope Results. VIII. Magnetic Field Structure near The Event Horizon","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.01173","snapshot_observed_at":"2026-08-06T16:40:19.061985Z","title":"Akiyama et al","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:19.061985Z"},"links":{"cited_paper":"/paper/2105.01173","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:5f17270eec9aef17fde8eb886f443b64f72e57e8a49e1bb8210612658cf314c3","observation_id":"f2c5e283-d4e7-49e1-91b8-d20410d5d8bf","resolution":{"observed_at":"2026-08-06T16:40:19.061985Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"astro-ph/9912263","last_updated":"1999-12-14T09:29:57Z","snapshot_observed_at":"2026-07-07T01:30:29.466209Z","submitted_at":"1999-12-14T09:29:57Z","title":"Viewing the Shadow of the Black Hole at the Galactic Center","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"astro-ph/9912263","snapshot_observed_at":"2026-08-06T16:40:19.177359Z","title":"Falcke, F","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:19.177359Z"},"links":{"cited_paper":"/paper/astro-ph/9912263","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:5e4ca74a437a17523db64c37a885dacaa54b3468d70439af776ffd590bdf8b74","observation_id":"163b6e43-e581-4ace-8269-71ffe432c0bd","resolution":{"observed_at":"2026-08-06T16:40:19.177359Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"astro-ph/9904193","last_updated":"2000-01-19T14:47:14Z","snapshot_observed_at":"2026-07-07T01:25:36.850012Z","submitted_at":"1999-04-15T12:35:30Z","title":"Schwarzschild black hole lensing","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"astro-ph/9904193","snapshot_observed_at":"2026-08-06T16:40:19.256446Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:19.256446Z"},"links":{"cited_paper":"/paper/astro-ph/9904193","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:9c9bd362a76a52b4cf04aeab0c85f3719884d2ebbdbb17c9ce6548fc75413f9a","observation_id":"d5b69bcb-27ae-492f-ac3e-1b41a4f231f1","resolution":{"observed_at":"2026-08-06T16:40:19.256446Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"gr-qc/0005050","last_updated":"2000-07-07T09:19:58Z","snapshot_observed_at":"2026-08-17T03:15:23.340720Z","submitted_at":"2000-05-15T22:45:13Z","title":"The geometry of photon surfaces","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"gr-qc/0005050","snapshot_observed_at":"2026-08-06T16:40:19.357836Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:19.357836Z"},"links":{"cited_paper":"/paper/gr-qc/0005050","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:505d4aec7d2c8c2ddfc4ae4f0d7f82c9e4993d28b0382a6bab16aa645dcae115","observation_id":"e06e8699-2511-4de9-8eed-0688f35254b1","resolution":{"observed_at":"2026-08-06T16:40:19.357836Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"gr-qc/0203049","last_updated":"2003-02-14T21:56:40Z","snapshot_observed_at":"2026-08-15T21:06:56.461494Z","submitted_at":"2002-03-13T19:26:51Z","title":"Reissner-Nordstrom black hole lensing","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"gr-qc/0203049","snapshot_observed_at":"2026-08-06T16:40:19.442714Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:19.442714Z"},"links":{"cited_paper":"/paper/gr-qc/0203049","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:f2aa4aa348b8301f32af85f307569ec4266d93b73bdd3885e3716226c82064e1","observation_id":"2d8d3a6d-f9b1-41cd-9f42-327ae2939790","resolution":{"observed_at":"2026-08-06T16:40:19.442714Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0810.2109","last_updated":"2008-10-12T15:53:51Z","snapshot_observed_at":"2026-08-15T10:04:36.196254Z","submitted_at":"2008-10-12T15:53:51Z","title":"Relativistic images of Schwarzschild black hole lensing","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0810.2109","snapshot_observed_at":"2026-08-06T16:40:19.570272Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:19.570272Z"},"links":{"cited_paper":"/paper/0810.2109","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:d21d38c2d581349758ad936fab489b6e11775a51a8e4204b124078e279de00fc","observation_id":"0b1ddaf5-1a51-4c48-ae14-b6edfc3a63e1","resolution":{"observed_at":"2026-08-06T16:40:19.570272Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1208.0635","last_updated":"2012-10-19T07:10:06Z","snapshot_observed_at":"2026-08-15T00:51:10.949203Z","submitted_at":"2012-08-03T00:33:25Z","title":"Shadows of Multi-Black Holes: Analytic Exploration","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1208.0635","snapshot_observed_at":"2026-08-06T16:40:19.662219Z","title":"Yumoto, D","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:19.662219Z"},"links":{"cited_paper":"/paper/1208.0635","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:da661861b6eb5d84d973fa10cacc0f2ab7a920ff2409ae9c13c99ddcd8e48a47","observation_id":"c9bea245-0110-41ea-b18b-fd3ed15a2dec","resolution":{"observed_at":"2026-08-06T16:40:19.662219Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1311.4251","last_updated":"2013-12-02T06:18:16Z","snapshot_observed_at":"2026-08-14T23:54:59.003143Z","submitted_at":"2013-11-18T03:11:21Z","title":"Observing the shadow of Einstein-Maxwell-Dilaton-Axion black hole","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1311.4251","snapshot_observed_at":"2026-08-06T16:40:19.753044Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:19.753044Z"},"links":{"cited_paper":"/paper/1311.4251","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:45ce9f9e232e7d2ceb10c46964e0839ba8c3b01ac76a0bdaa9c0662fc3c6d91e","observation_id":"636baeb3-42d5-4d61-bdbd-9aba215e4205","resolution":{"observed_at":"2026-08-06T16:40:19.753044Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1407.7457","last_updated":"2014-07-24T15:11:34Z","snapshot_observed_at":"2026-08-14T23:25:31.063319Z","submitted_at":"2014-07-24T15:11:34Z","title":"Constraints on a charge in the Reissner--Nordstr\\\"om metric for the black hole at the Galactic Center","version":1},"cited_work":{"arxiv_id":"1407.7457","doi":null,"metadata_source":"pith","pith_arxiv_id":"1407.7457","snapshot_observed_at":"2026-08-06T16:40:25.307717Z","title":"Constraints on a charge in the Reissner--Nordstr\\\"om metric for the black hole at the Galactic Center","venue":"gr-qc","work_id":"1c65c719-3b2b-4045-a930-be440a5a1a67","year":2014},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:19.846390Z"},"links":{"cited_paper":"/paper/1407.7457","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:baac6a3c1d743d847deef5e83a1c07fc49764d6c8a7ffb4a9c540fe436a54b76","observation_id":"20fa084b-a6d0-49eb-b444-6329be772379","resolution":{"observed_at":"2026-08-06T16:40:25.355896Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1506.03690","last_updated":"2015-06-17T11:29:45Z","snapshot_observed_at":"2026-08-14T22:44:50.149223Z","submitted_at":"2015-06-11T14:36:49Z","title":"Horizon structure of rotating Einstein-Born-Infeld black holes and shadow","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1506.03690","snapshot_observed_at":"2026-08-06T16:40:19.949326Z","title":"Atamurotov, S","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:19.949326Z"},"links":{"cited_paper":"/paper/1506.03690","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:f42638f43bf20bfe47d42397847b206b06692676a4135acefb58f22cb51edd18","observation_id":"d3b06040-2bdc-409a-8d2e-71d4c2e6b433","resolution":{"observed_at":"2026-08-06T16:40:19.949326Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1701.00079","last_updated":"2017-03-15T22:45:11Z","snapshot_observed_at":"2026-08-17T19:59:27.714975Z","submitted_at":"2016-12-31T09:26:51Z","title":"Shadows of Einstein-dilaton-Gauss-Bonnet black holes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1701.00079","snapshot_observed_at":"2026-08-06T16:40:20.039680Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.039680Z"},"links":{"cited_paper":"/paper/1701.00079","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:1f041a057f01cfbe5c41ac6728e154842d80678d30b258ed45effb3bd530bb79","observation_id":"73640067-d0d0-47b7-b95b-a7b97ce5f05f","resolution":{"observed_at":"2026-08-06T16:40:20.039680Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1610.09477","last_updated":"2016-10-29T09:11:41Z","snapshot_observed_at":"2026-08-16T11:56:35.823851Z","submitted_at":"2016-10-29T09:11:41Z","title":"Shadow of a Kerr-Sen dilaton-axion Black Hole","version":1},"cited_work":{"arxiv_id":"1610.09477","doi":null,"metadata_source":"pith","pith_arxiv_id":"1610.09477","snapshot_observed_at":"2026-08-06T16:40:25.202525Z","title":"Shadow of a Kerr-Sen dilaton-axion Black Hole","venue":"gr-qc","work_id":"223f357e-79e4-4d67-9107-25cac7eeed84","year":2016},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.130700Z"},"links":{"cited_paper":"/paper/1610.09477","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:5a15c93f07ba15e025685ac484b0b8de44b3f7e841c498bef2ff6d048140a08b","observation_id":"51fb56c5-2131-43df-9edc-47b8d60a5128","resolution":{"observed_at":"2026-08-06T16:40:25.236515Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1707.09521","last_updated":"2018-05-30T12:49:01Z","snapshot_observed_at":"2026-08-17T20:46:11.813686Z","submitted_at":"2017-07-29T14:45:17Z","title":"Shadows of rotating five-dimensional charged EMCS black holes","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1707.09521","snapshot_observed_at":"2026-08-06T16:40:20.233719Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.233719Z"},"links":{"cited_paper":"/paper/1707.09521","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:3aaa4ffbc033d97567ddd617b5ca94403eeb9a538ffbc321732a20a44cbda04e","observation_id":"daf3d931-5008-4535-8763-74491de7cdd4","resolution":{"observed_at":"2026-08-06T16:40:20.233719Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1707.09451","last_updated":"2017-10-08T04:13:27Z","snapshot_observed_at":"2026-08-14T20:44:31.704860Z","submitted_at":"2017-07-29T02:20:35Z","title":"Shadow casted by a Konoplya-Zhidenko rotating non-Kerr black hole","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1707.09451","snapshot_observed_at":"2026-08-06T16:40:20.346690Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.346690Z"},"links":{"cited_paper":"/paper/1707.09451","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:d416de5f11efc677458967f4414e54b43f06a50d38e5228be214189a7593afac","observation_id":"b5ee5272-b1c3-4d5b-b699-f27f1f357c05","resolution":{"observed_at":"2026-08-06T16:40:20.346690Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1807.00388","last_updated":"2018-10-11T08:46:03Z","snapshot_observed_at":"2026-08-14T18:57:01.044752Z","submitted_at":"2018-07-01T20:23:58Z","title":"Shadow cast and Deflection angle of Kerr-Newman-Kasuya spacetime","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1807.00388","snapshot_observed_at":"2026-08-06T16:40:20.469597Z","title":"¨Ovg¨ un, ˙I","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.469597Z"},"links":{"cited_paper":"/paper/1807.00388","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:0d66effa8ded111e0f06a0a1afb768dd617e6068505420f75114fd399f650a7b","observation_id":"03617546-e20c-46bf-bf67-956be2168781","resolution":{"observed_at":"2026-08-06T16:40:20.469597Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1804.04898","last_updated":"2018-04-13T11:54:34Z","snapshot_observed_at":"2026-08-14T19:26:17.672740Z","submitted_at":"2018-04-13T11:54:34Z","title":"Black hole shadow in an expanding universe with a cosmological constant","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1804.04898","snapshot_observed_at":"2026-08-06T16:40:20.595388Z","title":"Perlick, O","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.595388Z"},"links":{"cited_paper":"/paper/1804.04898","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:f8a6a60f763a455cf9ce66a7becd43cf68a9b4e414bc1f00bf45b7dacc501a10","observation_id":"c846ebd2-860e-4b32-a91f-54d460516e18","resolution":{"observed_at":"2026-08-06T16:40:20.595388Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1912.05154","last_updated":"2019-12-11T07:54:16Z","snapshot_observed_at":"2026-08-14T12:25:46.780833Z","submitted_at":"2019-12-11T07:54:16Z","title":"Shadow cast and deflection of light by charged rotating regular black holes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1912.05154","snapshot_observed_at":"2026-08-06T16:40:20.650408Z","title":"Kumar, S","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.650408Z"},"links":{"cited_paper":"/paper/1912.05154","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:d1b50821d8685a517c21ecd5fc4f6105ff60111b1f9d128f6fc9b5813e3dff59","observation_id":"6e04654b-dccb-4e1f-8dea-6f7313099860","resolution":{"observed_at":"2026-08-06T16:40:20.650408Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.05673","last_updated":"2019-08-18T06:22:33Z","snapshot_observed_at":"2026-08-17T05:16:36.439369Z","submitted_at":"2019-06-12T08:07:29Z","title":"Shadows and deflection angle of charged and slowly rotating black holes in Einstein-{\\AE}ther theory","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.05673","snapshot_observed_at":"2026-08-06T16:40:20.717550Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.717550Z"},"links":{"cited_paper":"/paper/1906.05673","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:fba337a172c2eaebbf0cf536fceaf2103e2c17bdece67d1e2b6e6f48a54daa2e","observation_id":"31f3b4cc-0f3f-4853-a96a-520cec2795c1","resolution":{"observed_at":"2026-08-06T16:40:20.717550Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:20.780508Z","title":"Ma and H","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.780508Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:f0f2be751f6781d4935ebad6b5d27c03971261d170e0a5b403958c8be0164883","observation_id":"99fe604c-9358-45ff-9fb1-a28e2d9825be","resolution":{"observed_at":"2026-08-06T16:40:20.780508Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1903.06376","last_updated":"2019-06-03T04:56:49Z","snapshot_observed_at":"2026-08-14T17:01:54.943304Z","submitted_at":"2019-03-15T06:02:40Z","title":"Understanding photon sphere and black hole shadow in dynamically evolving spacetimes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1903.06376","snapshot_observed_at":"2026-08-06T16:40:20.878366Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.878366Z"},"links":{"cited_paper":"/paper/1903.06376","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:762b47dcb7507e122d0e2a77bfec8813afd0cc3f0040b30d647f1dd34a32330a","observation_id":"b7ebefdb-7894-4748-b9a3-a87b2aa30a13","resolution":{"observed_at":"2026-08-06T16:40:20.878366Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2004.12074","last_updated":"2020-09-26T11:06:19Z","snapshot_observed_at":"2026-08-14T07:44:01.493804Z","submitted_at":"2020-04-25T07:45:05Z","title":"Shadows and photon spheres with spherical accretions in the four-dimensional Gauss-Bonnet black hole","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2004.12074","snapshot_observed_at":"2026-08-06T16:40:20.974330Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:20.974330Z"},"links":{"cited_paper":"/paper/2004.12074","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:4df05aa7cca627cac009bc859869577529dfbc3ecc069828fa323b430d44208b","observation_id":"8f66c063-1169-466d-8bd6-322659b3330d","resolution":{"observed_at":"2026-08-06T16:40:20.974330Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2007.06333","last_updated":"2020-07-17T02:27:46Z","snapshot_observed_at":"2026-08-14T17:44:24.443380Z","submitted_at":"2020-07-13T12:06:05Z","title":"Influence of quintessence dark energy on the shadow of black hole","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.06333","snapshot_observed_at":"2026-08-06T16:40:21.075720Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:21.075720Z"},"links":{"cited_paper":"/paper/2007.06333","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:1d670d26efbd625ff49aa57f475ed4491b3438f7c4127021d3f4f0332a61387a","observation_id":"c531b60d-231c-44ad-94d5-8ddd51169d2c","resolution":{"observed_at":"2026-08-06T16:40:21.075720Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2011.04310","last_updated":"2021-04-12T07:26:13Z","snapshot_observed_at":"2026-08-18T03:47:20.107005Z","submitted_at":"2020-11-09T10:33:12Z","title":"Image of a regular phantom compact object and its luminosity under spherical accretions","version":2},"cited_work":{"arxiv_id":"2011.04310","doi":null,"metadata_source":"pith","pith_arxiv_id":"2011.04310","snapshot_observed_at":"2026-08-06T16:40:24.930237Z","title":"Image of a regular phantom compact object and its luminosity under spherical accretions","venue":"gr-qc","work_id":"9d62ef73-3fe6-4322-a0fe-611a5b77a61a","year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:21.163625Z"},"links":{"cited_paper":"/paper/2011.04310","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:1a8f53b52260d69a880682d096f0b53d1b32f5e1eed330dbed5575ea08011304","observation_id":"8a2228c7-e3ad-4549-ba0a-9bc0ee2ce20b","resolution":{"observed_at":"2026-08-06T16:40:25.001070Z","resolver_source":"local_arxiv","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.10599","last_updated":"2021-05-21T13:54:20Z","snapshot_observed_at":"2026-08-10T14:39:55.184498Z","submitted_at":"2020-09-21T12:04:14Z","title":"Imprints of Dark Matter on Black Hole Shadows using Spherical Accretions","version":2},"cited_work":{"arxiv_id":"2009.10599","doi":null,"metadata_source":"pith","pith_arxiv_id":"2009.10599","snapshot_observed_at":"2026-08-06T16:40:24.751113Z","title":"Imprints of Dark Matter on Black Hole Shadows using Spherical Accretions","venue":"gr-qc","work_id":"ca36c78a-39e7-4734-84eb-cf214c602b52","year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:21.255695Z"},"links":{"cited_paper":"/paper/2009.10599","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:4dba4f6292dca91fd67b78187011cc0b046e2b151dc0456f1b35772570803dff","observation_id":"688ed247-ffb4-40da-abfd-e4675bf523ce","resolution":{"observed_at":"2026-08-06T16:40:24.831869Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2003.14107","last_updated":"2020-07-09T10:36:57Z","snapshot_observed_at":"2026-08-13T18:01:38.591790Z","submitted_at":"2020-03-31T11:27:32Z","title":"A study on black hole shadows in asymptotically de Sitter spacetimes","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.14107","snapshot_observed_at":"2026-08-06T16:40:21.364680Z","title":"Roy and S","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:21.364680Z"},"links":{"cited_paper":"/paper/2003.14107","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:0b735960923e4bdc85d0105251ae50e29b676c5709db400d38b67ee2ede10b46","observation_id":"65005446-52af-4741-abca-7fc5fae26187","resolution":{"observed_at":"2026-08-06T16:40:21.364680Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2001.04231","last_updated":"2020-04-09T05:17:01Z","snapshot_observed_at":"2026-08-09T10:49:12.879634Z","submitted_at":"2020-01-13T13:28:15Z","title":"Shadow of a Spinning Black Hole in an Expanding Universe","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2001.04231","snapshot_observed_at":"2026-08-06T16:40:21.474618Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:21.474618Z"},"links":{"cited_paper":"/paper/2001.04231","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:7ac82c6ff4343f50a781e12b58e0c28240271114b987c408fb2918f03ae89fe3","observation_id":"5352e78b-d738-45c7-85fd-532f5a949ad6","resolution":{"observed_at":"2026-08-06T16:40:21.474618Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2001.00460","last_updated":"2020-05-08T08:45:47Z","snapshot_observed_at":"2026-08-15T13:11:22.610030Z","submitted_at":"2020-01-02T14:42:47Z","title":"Gravitational deflection of light and shadow cast by rotating Kalb-Ramond black holes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2001.00460","snapshot_observed_at":"2026-08-06T16:40:21.546927Z","title":"Kumar, S","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:21.546927Z"},"links":{"cited_paper":"/paper/2001.00460","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:6790312ab6107d75031b0ce1d7d7f935fc670a149418aa927bd4b404d6b8e24d","observation_id":"e49ddcd3-a118-457e-8915-0afcb6433e6b","resolution":{"observed_at":"2026-08-06T16:40:21.546927Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.12194","last_updated":"2020-10-23T06:52:56Z","snapshot_observed_at":"2026-08-16T19:11:15.992206Z","submitted_at":"2020-10-23T06:52:56Z","title":"Shadows of the accelerating black holes","version":1},"cited_work":{"arxiv_id":"2010.12194","doi":null,"metadata_source":"pith","pith_arxiv_id":"2010.12194","snapshot_observed_at":"2026-08-06T16:40:24.555857Z","title":"Shadows of the accelerating black holes","venue":"gr-qc","work_id":"886613cc-8a7e-447a-b57b-c467df172f60","year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:21.639858Z"},"links":{"cited_paper":"/paper/2010.12194","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:ab83395d01f4a7271cbaa9ad15515be3e69b92b83d10a0e7df7eaa4ee7e84ed0","observation_id":"a910a0c5-0fb6-48a6-b112-89371420346b","resolution":{"observed_at":"2026-08-06T16:40:24.637037Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2022.13704","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:24.423673Z","title":null,"venue":null,"work_id":"2802a7a7-f855-40dd-b402-0ef9078cd771","year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:21.714496Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:7708865acc474bc1bb3d4cbbb10647d8514261971d8dfed6c090b681647cd568","observation_id":"6a4f7a25-624a-44f3-bfa6-3efb0ade467c","resolution":{"observed_at":"2026-08-06T16:40:24.475300Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2202.03809","last_updated":"2022-02-08T11:56:23Z","snapshot_observed_at":"2026-08-16T17:22:51.555175Z","submitted_at":"2022-02-08T11:56:23Z","title":"Light ring images of double photon spheres in black hole and wormhole space-times","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2202.03809","snapshot_observed_at":"2026-08-06T16:40:21.805303Z","title":"Guerrero, G","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:21.805303Z"},"links":{"cited_paper":"/paper/2202.03809","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:43d30a1cf5bf57c968771fcb131cb63a8f76ae9f3d00c362d080ea19636d5cc9","observation_id":"2b126cc1-b2bf-4393-a81c-06e0bf154109","resolution":{"observed_at":"2026-08-06T16:40:21.805303Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2204.01879","last_updated":"2022-09-09T22:30:45Z","snapshot_observed_at":"2026-08-16T17:09:19.587007Z","submitted_at":"2022-04-04T22:54:42Z","title":"Distortions of images of Schwarzschild lensing","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.01879","snapshot_observed_at":"2026-08-06T16:40:21.877470Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:21.877470Z"},"links":{"cited_paper":"/paper/2204.01879","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:724611e81c1d28388665c8b24bcca1da476e67109c0c0d1361dbc77762d09162","observation_id":"950e4d08-b60f-4672-9d54-74b5d28994da","resolution":{"observed_at":"2026-08-06T16:40:21.877470Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2104.08703","last_updated":"2021-05-03T14:38:52Z","snapshot_observed_at":"2026-08-16T18:30:49.658513Z","submitted_at":"2021-04-18T04:02:16Z","title":"Photon Spheres and Spherical Accretion Image of a Hairy Black Hole","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.08703","snapshot_observed_at":"2026-08-06T16:40:21.952323Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:21.952323Z"},"links":{"cited_paper":"/paper/2104.08703","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:75cff298cb168c292d5a9bd82a83449207f25a65872a583c408594eea17ca726","observation_id":"36441825-a989-46d9-b322-d402a631ff25","resolution":{"observed_at":"2026-08-06T16:40:21.952323Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.11770","last_updated":"2021-06-02T14:11:29Z","snapshot_observed_at":"2026-08-16T18:22:26.938949Z","submitted_at":"2021-05-25T09:11:34Z","title":"Photon Ring and Observational Appearance of a Hairy Black Hole","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.11770","snapshot_observed_at":"2026-08-06T16:40:22.062117Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.062117Z"},"links":{"cited_paper":"/paper/2105.11770","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:aba9a20ef7cf07d459a24a0af99cc92cabbf2bf085e98ee65faf963aa9c7d7d9","observation_id":"e7efba07-6052-47c8-8660-88095bfe3d7c","resolution":{"observed_at":"2026-08-06T16:40:22.062117Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1907.10876","last_updated":"2019-07-25T07:42:17Z","snapshot_observed_at":"2026-07-06T08:10:05.138655Z","submitted_at":"2019-07-25T07:42:17Z","title":"Quasi-topological Electromagnetism: Dark Energy, Dyonic Black Holes, Stable Photon Spheres and Hidden Electromagnetic Duality","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1907.10876","snapshot_observed_at":"2026-08-06T16:40:22.143241Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.143241Z"},"links":{"cited_paper":"/paper/1907.10876","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:8a2c8b852fd3a3608e41d48db4758b842cd90bf68affd030ec348a0c731a96c6","observation_id":"29740d4e-9e55-4611-b5a4-abf63dd629e4","resolution":{"observed_at":"2026-08-06T16:40:22.143241Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1011.1232","last_updated":"2010-11-08T18:31:49Z","snapshot_observed_at":"2026-08-15T05:03:53.059717Z","submitted_at":"2010-11-04T18:24:57Z","title":"Resummation of Massive Gravity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1011.1232","snapshot_observed_at":"2026-08-06T16:40:22.236917Z","title":"de Rham, G","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.236917Z"},"links":{"cited_paper":"/paper/1011.1232","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:42a11f19569d28adaeaa645d59b38fadb0e0fcd611453afee99abb0401af4bde","observation_id":"f69bb80e-05d4-4970-b70a-5043f33dbb6e","resolution":{"observed_at":"2026-08-06T16:40:22.236917Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2011.04032","last_updated":"2021-01-14T14:22:33Z","snapshot_observed_at":"2026-08-16T19:07:22.313831Z","submitted_at":"2020-11-08T17:30:55Z","title":"Gravitational wave echoes from black holes in massive gravity","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2011.04032","snapshot_observed_at":"2026-08-06T16:40:22.333626Z","title":"Dong and D","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.333626Z"},"links":{"cited_paper":"/paper/2011.04032","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:0515052e41abf4be235e11d10b38c49903f4bec3cae2fac2d95c46ab0c96cf93","observation_id":"27bfcb62-43bb-475c-8864-dce5f8dca235","resolution":{"observed_at":"2026-08-06T16:40:22.333626Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2112.14133","last_updated":"2022-01-06T11:21:00Z","snapshot_observed_at":"2026-08-16T17:31:36.905668Z","submitted_at":"2021-12-28T13:22:20Z","title":"Quasinormal Modes of Black Holes with Multiple Photon Spheres","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2112.14133","snapshot_observed_at":"2026-08-06T16:40:22.408740Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.408740Z"},"links":{"cited_paper":"/paper/2112.14133","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:3bf609743e617c9931d8685a75f07acfb72692ef32cffdcb8bcbe81b0c1c4897","observation_id":"c225b75c-001f-4669-870c-a40bf91d0141","resolution":{"observed_at":"2026-08-06T16:40:22.408740Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2204.00982","last_updated":"2022-04-20T15:39:30Z","snapshot_observed_at":"2026-08-16T17:09:42.861543Z","submitted_at":"2022-04-03T04:00:59Z","title":"Echoes from Hairy Black Holes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.00982","snapshot_observed_at":"2026-08-06T16:40:22.514249Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.514249Z"},"links":{"cited_paper":"/paper/2204.00982","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:3b08d3c8ce5c60a7a8011b172641f3690c240bbbf1ed8ef9454d4f3993a801f5","observation_id":"585811f1-2ec0-418e-aab6-98f9de94e989","resolution":{"observed_at":"2026-08-06T16:40:22.514249Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2112.14780","last_updated":"2021-12-29T19:00:01Z","snapshot_observed_at":"2026-08-16T17:31:16.799349Z","submitted_at":"2021-12-29T19:00:01Z","title":"Echoes from Classical Black Holes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2112.14780","snapshot_observed_at":"2026-08-06T16:40:22.620665Z","title":"Huang, M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.620665Z"},"links":{"cited_paper":"/paper/2112.14780","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:a2180e7625e3eb1040b89d200e376cfd4af306c6f5ed9d4cb919f4206bac82c7","observation_id":"8444f5e8-0152-4776-a6ac-d989820a067e","resolution":{"observed_at":"2026-08-06T16:40:22.620665Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2023.10139","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:24.096847Z","title":null,"venue":null,"work_id":"56e692f4-5350-4080-99ce-7fafbc1e705f","year":2024},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.691149Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:af6c464804faab98a3c42cb1573184f04139941963ca5d118d2c67a0276c6c59","observation_id":"be647b81-a2a5-4d8b-8faf-8829fc8966c3","resolution":{"observed_at":"2026-08-06T16:40:24.183595Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2112.10109","last_updated":"2021-12-19T10:30:36Z","snapshot_observed_at":"2026-08-17T09:16:32.130248Z","submitted_at":"2021-12-19T10:30:36Z","title":"Signature of Non-uniform Area Quantization on Black Hole Echoes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2112.10109","snapshot_observed_at":"2026-08-06T16:40:22.746355Z","title":"Chakravarti, R","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.746355Z"},"links":{"cited_paper":"/paper/2112.10109","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:b043b5a6a84c53cd46b28726a98f66d52f18f5264e9ba417a7bc6ede277fb9a5","observation_id":"0f05a6c1-c172-4d56-973e-b00ebef474d6","resolution":{"observed_at":"2026-08-06T16:40:22.746355Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1904.05652","last_updated":"2019-04-11T12:10:13Z","snapshot_observed_at":"2026-08-16T12:09:23.537490Z","submitted_at":"2019-04-11T12:10:13Z","title":"Mixing of gravitational wave echoes","version":1},"cited_work":{"arxiv_id":"1904.05652","doi":null,"metadata_source":"pith","pith_arxiv_id":"1904.05652","snapshot_observed_at":"2026-08-06T16:40:23.919134Z","title":"Mixing of gravitational wave echoes","venue":"gr-qc","work_id":"73c61ca5-8d58-49b8-8b11-36941ba446e1","year":2019},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.825478Z"},"links":{"cited_paper":"/paper/1904.05652","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:c86fe6abe43f6b772b1df48f9c7fe2ba723b9501cc5719a163894d76cbdca77f","observation_id":"422c7f2c-4a86-415e-8418-3a4b89ade910","resolution":{"observed_at":"2026-08-06T16:40:23.972110Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2106.13486","last_updated":"2021-08-27T01:20:18Z","snapshot_observed_at":"2026-08-16T18:14:34.108399Z","submitted_at":"2021-06-25T07:59:11Z","title":"Black Holes With Many Horizons in the Theories of Nonlinear Electrodynamics","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.13486","snapshot_observed_at":"2026-08-06T16:40:22.903010Z","title":"Gao, Black holes with many horizons in the theories of nonlinear electrodynamics, Phys","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.903010Z"},"links":{"cited_paper":"/paper/2106.13486","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:c8a1232310500b73049436d9ee6f8ce2b228c4b059f84ae95001056301889446","observation_id":"cf6c1d70-08c1-41d4-8747-b22fb324bb69","resolution":{"observed_at":"2026-08-06T16:40:22.903010Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:22.957599Z","title":"Born, On the quantum theory of the electromagnetic field, Proc","venue":null,"work_id":null,"year":1934},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:22.957599Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:6af258b09252cef28410ecaabf5bac75c82ded24a99d36ddf7fb0dfc2922553a","observation_id":"ecd3fbc9-b2e0-4a53-a925-b593fd3a2435","resolution":{"observed_at":"2026-08-06T16:40:22.957599Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T16:40:23.036969Z","title":"Born and L","venue":null,"work_id":null,"year":1934},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:23.036969Z"},"links":{"citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:e9e9f1e0ce2459177cb408495e9c7b1a28fc9b8de3aa1433804e7199ceaf6075","observation_id":"8fd3bb37-4ae3-4b6d-9013-cf815f38983f","resolution":{"observed_at":"2026-08-06T16:40:23.036969Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1305.4790","last_updated":"2013-08-06T07:10:09Z","snapshot_observed_at":"2026-08-17T20:27:33.750416Z","submitted_at":"2013-05-21T11:54:15Z","title":"Non-singular quantum-inspired gravitational collapse","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1305.4790","snapshot_observed_at":"2026-08-06T16:40:23.114311Z","title":"Bambi, D","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:23.114311Z"},"links":{"cited_paper":"/paper/1305.4790","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:c5f95c30974a4df5895b36ca4f1833f6b700548282b4b0f82b2477f805232c97","observation_id":"5f3ec860-9533-416c-9cc2-29d8d4778122","resolution":{"observed_at":"2026-08-06T16:40:23.114311Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2209.02559","last_updated":"2022-10-04T08:15:10Z","snapshot_observed_at":"2026-08-16T16:34:26.073700Z","submitted_at":"2022-09-06T15:11:01Z","title":"Splitting the Echoes of Black Holes in Einstein-nonlinear Electrodynamic Theories","version":2},"cited_work":{"arxiv_id":"2209.02559","doi":null,"metadata_source":"pith","pith_arxiv_id":"2209.02559","snapshot_observed_at":"2026-08-06T16:40:23.649320Z","title":"Splitting the Echoes of Black Holes in Einstein-nonlinear Electrodynamic Theories","venue":"gr-qc","work_id":"9772f360-12cd-4464-b3c3-8a3695dc42ee","year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:23.200020Z"},"links":{"cited_paper":"/paper/2209.02559","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:5eef1e4e08e768dd54b90f7058338d9e4ce9030fa5ee2237426d2c1792159558","observation_id":"3f60b40a-64d5-4fae-a8cb-36d53b06b360","resolution":{"observed_at":"2026-08-06T16:40:23.709463Z","resolver_source":"local_arxiv","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.13948","last_updated":"2022-05-07T15:06:32Z","snapshot_observed_at":"2026-08-16T17:03:44.775212Z","submitted_at":"2022-04-29T08:47:56Z","title":"Gravitational Lensing by Black Holes with Multiple Photon Spheres","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.13948","snapshot_observed_at":"2026-08-06T16:40:23.286384Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:23.286384Z"},"links":{"cited_paper":"/paper/2204.13948","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:e6bb9b8f26efac3ee24b5220df11c5dfed5ba74281236fde81ab414cbeda56e9","observation_id":"050ac179-feeb-43d0-b76f-d9030ba5e09f","resolution":{"observed_at":"2026-08-06T16:40:23.286384Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.00873","last_updated":"2019-06-17T16:03:08Z","snapshot_observed_at":"2026-08-14T16:21:49.374613Z","submitted_at":"2019-06-03T15:29:09Z","title":"Black Hole Shadows, Photon Rings, and Lensing Rings","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.00873","snapshot_observed_at":"2026-08-06T16:40:23.380584Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-06T16:40:23.380584Z"},"links":{"cited_paper":"/paper/1906.00873","citing_paper":"/paper/2507.13048"},"observation_digest":"sha256:5d11f57fcf110bb088639ed3b0969736d1d92f4b8a636e42a4db35cc7e309eb4","observation_id":"fb5db750-4ce9-43af-b9a9-72992b99d679","resolution":{"observed_at":"2026-08-06T16:40:23.380584Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.13048","last_updated":"2025-07-17T12:21:04Z","latest_version":1,"primary_category":"gr-qc","snapshot_observed_at":"2026-08-16T18:56:56.959757Z","submitted_at":"2025-07-17T12:21:04Z","title":"Gravitational Lensing by Black Holes in Einstein-nonlinear Electrodynamic Theories with Multiple Photon Spheres"},"reference_resolution":{"displayed":85,"state_counts":{"malformed_identifier":6,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":65,"verified_exact":12,"verified_fuzzy":0},"total_outbound_references":85},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 85 of 85 outbound references and 2 inbound Pith citation observations for arXiv:2507.13048."}