{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:TKGLTKP4Y6RK6XV26H3MHFHKF5","short_pith_number":"pith:TKGLTKP4","canonical_record":{"source":{"id":"0708.0178","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2007-08-01T15:31:22Z","cross_cats_sorted":[],"title_canon_sha256":"69aa29429f4430be7fc9379b7f0bbeeb25b62f42080debb029d2ef516f2c5323","abstract_canon_sha256":"d4727591a7b79c864a7a376ec129de97ee4c913c45be11a8e486e2d768750367"},"schema_version":"1.0"},"canonical_sha256":"9a8cb9a9fcc7a2af5ebaf1f6c394ea2f64f23cc23a945b2dbef5abc96d405346","source":{"kind":"arxiv","id":"0708.0178","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.0178","created_at":"2026-05-18T00:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"0708.0178v1","created_at":"2026-05-18T00:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.0178","created_at":"2026-05-18T00:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"TKGLTKP4Y6RK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TKGLTKP4Y6RK6XV2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TKGLTKP4","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:TKGLTKP4Y6RK6XV26H3MHFHKF5","target":"record","payload":{"canonical_record":{"source":{"id":"0708.0178","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2007-08-01T15:31:22Z","cross_cats_sorted":[],"title_canon_sha256":"69aa29429f4430be7fc9379b7f0bbeeb25b62f42080debb029d2ef516f2c5323","abstract_canon_sha256":"d4727591a7b79c864a7a376ec129de97ee4c913c45be11a8e486e2d768750367"},"schema_version":"1.0"},"canonical_sha256":"9a8cb9a9fcc7a2af5ebaf1f6c394ea2f64f23cc23a945b2dbef5abc96d405346","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:32.999131Z","signature_b64":"6Wux4RHxH1o9FAWQC/8Jd9MPmAUNP5lihXd6IgpcqLeKR0jMyDQjEP5o5YGdTfAVHxl9K0hcZCAgiWRNZFpYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a8cb9a9fcc7a2af5ebaf1f6c394ea2f64f23cc23a945b2dbef5abc96d405346","last_reissued_at":"2026-05-18T00:59:32.998632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:32.998632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0708.0178","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":"2026-05-18T00:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rWTAT0E48DwjhGxR0HDx90zZPkJuE3pts1eBghvjBOFM/L4ATjlq9kNIcK1MiZtoeQn31BZU+WgEM6DWJ6Q2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:21:58.291133Z"},"content_sha256":"93fe7ae2c8bcc6991eb047e0df6d47b1477cf19c8375f718bae1c111461bdaed","schema_version":"1.0","event_id":"sha256:93fe7ae2c8bcc6991eb047e0df6d47b1477cf19c8375f718bae1c111461bdaed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:TKGLTKP4Y6RK6XV26H3MHFHKF5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theoretical gravitational lensing. Beyond the weak-field small-angle approximation","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Volker Perlick","submitted_at":"2007-08-01T15:31:22Z","abstract_excerpt":"An overview is given on those theoretical gravitational lensing results that can be formulated in a spacetime setting, without assuming that the gravitational fields are weak and that the bending angles are small. The first part is devoted to analytical methods considering spacetimes in which the equations for light rays (lightlike geodesics) is completely integrable. This includes spherically symmetric static spacetimes, the Kerr spacetime and plane gravitational waves. The second part is devoted to qualitative methods which give some information on lensing properties without actually solving"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0178","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":"2026-05-18T00:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tL5uxFb0f1rbO1/Qor4Kdrkku10QgdgJyaT94DowTpFq/9CWLwRwzv5Xoqzzx6+xifykIF4JNsnDzPQDEQrUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:21:58.291932Z"},"content_sha256":"fabdd6f90f2b5eaa92f3615a4849178d2397ae083ca5de026836616e87e59ab4","schema_version":"1.0","event_id":"sha256:fabdd6f90f2b5eaa92f3615a4849178d2397ae083ca5de026836616e87e59ab4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKGLTKP4Y6RK6XV26H3MHFHKF5/bundle.json","state_url":"https://pith.science/pith/TKGLTKP4Y6RK6XV26H3MHFHKF5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKGLTKP4Y6RK6XV26H3MHFHKF5/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":"2026-06-05T19:21:58Z","links":{"resolver":"https://pith.science/pith/TKGLTKP4Y6RK6XV26H3MHFHKF5","bundle":"https://pith.science/pith/TKGLTKP4Y6RK6XV26H3MHFHKF5/bundle.json","state":"https://pith.science/pith/TKGLTKP4Y6RK6XV26H3MHFHKF5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKGLTKP4Y6RK6XV26H3MHFHKF5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:TKGLTKP4Y6RK6XV26H3MHFHKF5","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":"d4727591a7b79c864a7a376ec129de97ee4c913c45be11a8e486e2d768750367","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2007-08-01T15:31:22Z","title_canon_sha256":"69aa29429f4430be7fc9379b7f0bbeeb25b62f42080debb029d2ef516f2c5323"},"schema_version":"1.0","source":{"id":"0708.0178","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.0178","created_at":"2026-05-18T00:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"0708.0178v1","created_at":"2026-05-18T00:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.0178","created_at":"2026-05-18T00:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"TKGLTKP4Y6RK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"TKGLTKP4Y6RK6XV2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"TKGLTKP4","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:fabdd6f90f2b5eaa92f3615a4849178d2397ae083ca5de026836616e87e59ab4","target":"graph","created_at":"2026-05-18T00:59:32Z","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":"An overview is given on those theoretical gravitational lensing results that can be formulated in a spacetime setting, without assuming that the gravitational fields are weak and that the bending angles are small. The first part is devoted to analytical methods considering spacetimes in which the equations for light rays (lightlike geodesics) is completely integrable. This includes spherically symmetric static spacetimes, the Kerr spacetime and plane gravitational waves. The second part is devoted to qualitative methods which give some information on lensing properties without actually solving","authors_text":"Volker Perlick","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2007-08-01T15:31:22Z","title":"Theoretical gravitational lensing. Beyond the weak-field small-angle approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0178","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":"sha256:93fe7ae2c8bcc6991eb047e0df6d47b1477cf19c8375f718bae1c111461bdaed","target":"record","created_at":"2026-05-18T00:59:32Z","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":"d4727591a7b79c864a7a376ec129de97ee4c913c45be11a8e486e2d768750367","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2007-08-01T15:31:22Z","title_canon_sha256":"69aa29429f4430be7fc9379b7f0bbeeb25b62f42080debb029d2ef516f2c5323"},"schema_version":"1.0","source":{"id":"0708.0178","kind":"arxiv","version":1}},"canonical_sha256":"9a8cb9a9fcc7a2af5ebaf1f6c394ea2f64f23cc23a945b2dbef5abc96d405346","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a8cb9a9fcc7a2af5ebaf1f6c394ea2f64f23cc23a945b2dbef5abc96d405346","first_computed_at":"2026-05-18T00:59:32.998632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:32.998632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Wux4RHxH1o9FAWQC/8Jd9MPmAUNP5lihXd6IgpcqLeKR0jMyDQjEP5o5YGdTfAVHxl9K0hcZCAgiWRNZFpYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:32.999131Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.0178","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93fe7ae2c8bcc6991eb047e0df6d47b1477cf19c8375f718bae1c111461bdaed","sha256:fabdd6f90f2b5eaa92f3615a4849178d2397ae083ca5de026836616e87e59ab4"],"state_sha256":"22bcca052c42dc22a343d07cf84a4c63309f934cd269694ccb877358fd4b4f64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AsqjP+J5+XdwCuA+FhekIzFW2EbNo849XepJ3ymvWpDhsR69vBBQGxOioU9qFZO45K011Q32kTzl1bCcom+NDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:21:58.298172Z","bundle_sha256":"09cd49d4fdd161453f0493dc176f5c6fd8e130f8a7293193b09568b27bd585d9"}}