{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:WKQ435EVVUE5PE767SR4KIBGGG","short_pith_number":"pith:WKQ435EV","schema_version":"1.0","canonical_sha256":"b2a1cdf495ad09d793fefca3c5202631884a221f8eac3fa1792146b94640e661","source":{"kind":"arxiv","id":"2204.01879","version":2},"attestation_state":"computed","paper":{"title":"Distortions of images of Schwarzschild lensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","astro-ph.GA","astro-ph.HE","hep-th"],"primary_cat":"gr-qc","authors_text":"K. S. Virbhadra","submitted_at":"2022-04-04T22:54:42Z","abstract_excerpt":"We model the supermassive dark object $M87^*$ as a Schwarzschild lens and study the variations in tangential, radial, and total (the product of tangential and radial) magnifications of images (primary, secondary, and relativistic) against the changes in angular source position and the ratio of lens-source to the observer-source distance. Further, we study the behavior of partial derivatives (with respect to the angular source position) of total magnifications of images against the angular source position. Finally, we model supermassive dark objects at centers of 40 galaxies as Schwarzschild le"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2204.01879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-04-04T22:54:42Z","cross_cats_sorted":["astro-ph.CO","astro-ph.GA","astro-ph.HE","hep-th"],"title_canon_sha256":"2cea4de35177d0a242c862ecb1835cb88390664cb16dc7403b361ebb99dea81d","abstract_canon_sha256":"e5bb21975cdc7650d3732b9cf510e42c550ebfd83ee7078767ed889f1cd9ede2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:00:00.224235Z","signature_b64":"bBWg3Fecs8p++D2zpuF5ZB3yXObPJ7+6YBpNo/STapNnOy5VH2jAM21Bw7Z/Tz+lKMknZ2wu7lnCPWXc/t50Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2a1cdf495ad09d793fefca3c5202631884a221f8eac3fa1792146b94640e661","last_reissued_at":"2026-07-05T05:00:00.223835Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:00:00.223835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distortions of images of Schwarzschild lensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","astro-ph.GA","astro-ph.HE","hep-th"],"primary_cat":"gr-qc","authors_text":"K. S. Virbhadra","submitted_at":"2022-04-04T22:54:42Z","abstract_excerpt":"We model the supermassive dark object $M87^*$ as a Schwarzschild lens and study the variations in tangential, radial, and total (the product of tangential and radial) magnifications of images (primary, secondary, and relativistic) against the changes in angular source position and the ratio of lens-source to the observer-source distance. Further, we study the behavior of partial derivatives (with respect to the angular source position) of total magnifications of images against the angular source position. Finally, we model supermassive dark objects at centers of 40 galaxies as Schwarzschild le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.01879","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.01879/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2204.01879","created_at":"2026-07-05T05:00:00.223889+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.01879v2","created_at":"2026-07-05T05:00:00.223889+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.01879","created_at":"2026-07-05T05:00:00.223889+00:00"},{"alias_kind":"pith_short_12","alias_value":"WKQ435EVVUE5","created_at":"2026-07-05T05:00:00.223889+00:00"},{"alias_kind":"pith_short_16","alias_value":"WKQ435EVVUE5PE76","created_at":"2026-07-05T05:00:00.223889+00:00"},{"alias_kind":"pith_short_8","alias_value":"WKQ435EV","created_at":"2026-07-05T05:00:00.223889+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.27170","citing_title":"Regular black hole solutions and the quark chemical potential at the QCD phase transition","ref_index":38,"is_internal_anchor":false},{"citing_arxiv_id":"2509.03584","citing_title":"Unveiling horizons in quantum critical collapse","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2509.03584","citing_title":"Unveiling horizons in quantum critical collapse","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2601.06864","citing_title":"Boundary-only weak deflection angles from isothermal optical geometry","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2602.04593","citing_title":"Emergent Hawking Radiation and Quantum Sensing in a Quenched Chiral Spin Chain","ref_index":28,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WKQ435EVVUE5PE767SR4KIBGGG","json":"https://pith.science/pith/WKQ435EVVUE5PE767SR4KIBGGG.json","graph_json":"https://pith.science/api/pith-number/WKQ435EVVUE5PE767SR4KIBGGG/graph.json","events_json":"https://pith.science/api/pith-number/WKQ435EVVUE5PE767SR4KIBGGG/events.json","paper":"https://pith.science/paper/WKQ435EV"},"agent_actions":{"view_html":"https://pith.science/pith/WKQ435EVVUE5PE767SR4KIBGGG","download_json":"https://pith.science/pith/WKQ435EVVUE5PE767SR4KIBGGG.json","view_paper":"https://pith.science/paper/WKQ435EV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.01879&json=true","fetch_graph":"https://pith.science/api/pith-number/WKQ435EVVUE5PE767SR4KIBGGG/graph.json","fetch_events":"https://pith.science/api/pith-number/WKQ435EVVUE5PE767SR4KIBGGG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WKQ435EVVUE5PE767SR4KIBGGG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WKQ435EVVUE5PE767SR4KIBGGG/action/storage_attestation","attest_author":"https://pith.science/pith/WKQ435EVVUE5PE767SR4KIBGGG/action/author_attestation","sign_citation":"https://pith.science/pith/WKQ435EVVUE5PE767SR4KIBGGG/action/citation_signature","submit_replication":"https://pith.science/pith/WKQ435EVVUE5PE767SR4KIBGGG/action/replication_record"}},"created_at":"2026-07-05T05:00:00.223889+00:00","updated_at":"2026-07-05T05:00:00.223889+00:00"}