{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7OICEYM4EXU2VFW7GAICM6CGCA","short_pith_number":"pith:7OICEYM4","canonical_record":{"source":{"id":"1507.08545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-24T15:25:34Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"b3c6f3f6477f0df14edb8375b9753c0c7b9043692e3efcdaa2dfd1b25f390a65","abstract_canon_sha256":"aa61b4084cea2e392b1c594cb1d385c74eb5531382d8b8586b8332fbb85d78c9"},"schema_version":"1.0"},"canonical_sha256":"fb9022619c25e9aa96df3010267846102e5a66f54e86da1a2b1eed3fc3e21f14","source":{"kind":"arxiv","id":"1507.08545","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08545","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08545v1","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08545","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"7OICEYM4EXU2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7OICEYM4EXU2VFW7","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7OICEYM4","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7OICEYM4EXU2VFW7GAICM6CGCA","target":"record","payload":{"canonical_record":{"source":{"id":"1507.08545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-24T15:25:34Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"b3c6f3f6477f0df14edb8375b9753c0c7b9043692e3efcdaa2dfd1b25f390a65","abstract_canon_sha256":"aa61b4084cea2e392b1c594cb1d385c74eb5531382d8b8586b8332fbb85d78c9"},"schema_version":"1.0"},"canonical_sha256":"fb9022619c25e9aa96df3010267846102e5a66f54e86da1a2b1eed3fc3e21f14","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:06.154352Z","signature_b64":"VN2vs6DBC4jwditLYP23VjDVGqzgUXajUb/CJb1WB/+Ut73dgGc5+seXiK7z0STSHcD5oT/jdQQ5mz8Lvbl1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb9022619c25e9aa96df3010267846102e5a66f54e86da1a2b1eed3fc3e21f14","last_reissued_at":"2026-05-18T01:36:06.153838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:06.153838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.08545","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7TlwEcRddosVVzOS4crHQh8h0VgTxNHmSKpiw4tBsl/znFRjRmkc5rAwOvsd+tVVWcjGisW1nB9m2+ydLhVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:17:57.266629Z"},"content_sha256":"385bec8e9c869e531a1d9cabe6479547fb8d85b1eb05fcce584c58b003ffb515","schema_version":"1.0","event_id":"sha256:385bec8e9c869e531a1d9cabe6479547fb8d85b1eb05fcce584c58b003ffb515"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7OICEYM4EXU2VFW7GAICM6CGCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gravitational Lensing in Plasmic Medium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO"],"primary_cat":"gr-qc","authors_text":"G. S. Bisnovatyi-Kogan, O. Yu. Tsupko","submitted_at":"2015-07-24T15:25:34Z","abstract_excerpt":"The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08545","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vMhT0PpwYxO5z3xxL81YCgGjX5SkQWIoFId1ZkZU8PkDyoYg+ZSSaVYx36/3nyKDDkqDiA5bhup1Xhf3ZcX/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T23:17:57.267226Z"},"content_sha256":"e3d5d77003a6a6a14b81855a09ba1081082ff285d21bf51ead4dd8f67c4d6bf2","schema_version":"1.0","event_id":"sha256:e3d5d77003a6a6a14b81855a09ba1081082ff285d21bf51ead4dd8f67c4d6bf2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7OICEYM4EXU2VFW7GAICM6CGCA/bundle.json","state_url":"https://pith.science/pith/7OICEYM4EXU2VFW7GAICM6CGCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7OICEYM4EXU2VFW7GAICM6CGCA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T23:17:57Z","links":{"resolver":"https://pith.science/pith/7OICEYM4EXU2VFW7GAICM6CGCA","bundle":"https://pith.science/pith/7OICEYM4EXU2VFW7GAICM6CGCA/bundle.json","state":"https://pith.science/pith/7OICEYM4EXU2VFW7GAICM6CGCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7OICEYM4EXU2VFW7GAICM6CGCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7OICEYM4EXU2VFW7GAICM6CGCA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"aa61b4084cea2e392b1c594cb1d385c74eb5531382d8b8586b8332fbb85d78c9","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-24T15:25:34Z","title_canon_sha256":"b3c6f3f6477f0df14edb8375b9753c0c7b9043692e3efcdaa2dfd1b25f390a65"},"schema_version":"1.0","source":{"id":"1507.08545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08545","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08545v1","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08545","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"7OICEYM4EXU2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7OICEYM4EXU2VFW7","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7OICEYM4","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:e3d5d77003a6a6a14b81855a09ba1081082ff285d21bf51ead4dd8f67c4d6bf2","target":"graph","created_at":"2026-05-18T01:36:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhom","authors_text":"G. S. Bisnovatyi-Kogan, O. Yu. Tsupko","cross_cats":["astro-ph.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-24T15:25:34Z","title":"Gravitational Lensing in Plasmic Medium"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08545","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:385bec8e9c869e531a1d9cabe6479547fb8d85b1eb05fcce584c58b003ffb515","target":"record","created_at":"2026-05-18T01:36:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"aa61b4084cea2e392b1c594cb1d385c74eb5531382d8b8586b8332fbb85d78c9","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-07-24T15:25:34Z","title_canon_sha256":"b3c6f3f6477f0df14edb8375b9753c0c7b9043692e3efcdaa2dfd1b25f390a65"},"schema_version":"1.0","source":{"id":"1507.08545","kind":"arxiv","version":1}},"canonical_sha256":"fb9022619c25e9aa96df3010267846102e5a66f54e86da1a2b1eed3fc3e21f14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb9022619c25e9aa96df3010267846102e5a66f54e86da1a2b1eed3fc3e21f14","first_computed_at":"2026-05-18T01:36:06.153838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:06.153838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VN2vs6DBC4jwditLYP23VjDVGqzgUXajUb/CJb1WB/+Ut73dgGc5+seXiK7z0STSHcD5oT/jdQQ5mz8Lvbl1Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:06.154352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:385bec8e9c869e531a1d9cabe6479547fb8d85b1eb05fcce584c58b003ffb515","sha256:e3d5d77003a6a6a14b81855a09ba1081082ff285d21bf51ead4dd8f67c4d6bf2"],"state_sha256":"fb4220a25ee2e40986f14798b6364104422ef45423b9c517675152bce94c8da6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KfNZVVlYlu8gI+9oXiUeoeZSJguDuYLxmRF4IAbR+8EqGxz3eydXUeuRFp6g2m8ehz2yZqX+oK8mbZaxGaCIBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T23:17:57.270889Z","bundle_sha256":"5817aba52013fcfe66931972cb22c545859f0efff8cd29a24220169d621b2081"}}