{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZR4OALQRNLSS66YN3HAVK66ZJ4","short_pith_number":"pith:ZR4OALQR","canonical_record":{"source":{"id":"1504.07854","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-04-29T13:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"56c7272427e236b2b8c581f754055b5de611f3d5bcad150ce8251525c6172253","abstract_canon_sha256":"de4b710c213ec79fa90d99604a1aa7be5eac418e09aad1cf561a09192a4790e8"},"schema_version":"1.0"},"canonical_sha256":"cc78e02e116ae52f7b0dd9c1557bd94f08051f1040380b8cf6945b2e55055e4d","source":{"kind":"arxiv","id":"1504.07854","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07854","created_at":"2026-05-18T01:35:10Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07854v2","created_at":"2026-05-18T01:35:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07854","created_at":"2026-05-18T01:35:10Z"},{"alias_kind":"pith_short_12","alias_value":"ZR4OALQRNLSS","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZR4OALQRNLSS66YN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZR4OALQR","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZR4OALQRNLSS66YN3HAVK66ZJ4","target":"record","payload":{"canonical_record":{"source":{"id":"1504.07854","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-04-29T13:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"56c7272427e236b2b8c581f754055b5de611f3d5bcad150ce8251525c6172253","abstract_canon_sha256":"de4b710c213ec79fa90d99604a1aa7be5eac418e09aad1cf561a09192a4790e8"},"schema_version":"1.0"},"canonical_sha256":"cc78e02e116ae52f7b0dd9c1557bd94f08051f1040380b8cf6945b2e55055e4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:10.206864Z","signature_b64":"6z//j86RMoU/oYvQnYtYD3snQOGeeYestzdXhYC1cn7jGsN9dUDxYB0LfXYaTlov8EsS9ywqILqvAyBmR0CODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc78e02e116ae52f7b0dd9c1557bd94f08051f1040380b8cf6945b2e55055e4d","last_reissued_at":"2026-05-18T01:35:10.206249Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:10.206249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.07854","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:35:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FDAej89jow4Zh2035fPhtC2rx81Pr/1BsbrFh/wjpRdXHpQGPm0SyicqJPX+fGRxCmuMw0DwEywLYUsKyj+hDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:11:01.121122Z"},"content_sha256":"f7044d77e4a88c28110001c90f96dc04e41010e4d1b9045a08c8975ca59ae379","schema_version":"1.0","event_id":"sha256:f7044d77e4a88c28110001c90f96dc04e41010e4d1b9045a08c8975ca59ae379"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZR4OALQRNLSS66YN3HAVK66ZJ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytical solutions of the geodesic equation in the spacetime of a black hole in f(R) gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Claus L\\\"ammerzahl, Jutta Kunz, Reza Saffari, Saheb Soroushfar","submitted_at":"2015-04-29T13:35:06Z","abstract_excerpt":"We consider the motion of test particles in the spacetime of a black hole in f(R) gravity. The complete set of analytic solutions of the geodesic equation in the spacetime of this black hole are presented. The geodesic equations are solved in terms of Weierstrass elliptic functions and derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant $\\Lambda$ and the real constant $\\beta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07854","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":""},"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":"2026-05-18T01:35:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CB0kCxExcgeoXM5VlsFF9xJPBeJzu3cZyHhOtrOuuRMKDpe2w0vkYIKMBGqYKuIrOsvHsO3j91+Vm+FlGvIlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:11:01.121510Z"},"content_sha256":"2266acff6b5a54f368a0cf30b6fe40e6d88a81cbb9f38e7cd31a3c779bbc9300","schema_version":"1.0","event_id":"sha256:2266acff6b5a54f368a0cf30b6fe40e6d88a81cbb9f38e7cd31a3c779bbc9300"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZR4OALQRNLSS66YN3HAVK66ZJ4/bundle.json","state_url":"https://pith.science/pith/ZR4OALQRNLSS66YN3HAVK66ZJ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZR4OALQRNLSS66YN3HAVK66ZJ4/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":"2026-05-26T19:11:01Z","links":{"resolver":"https://pith.science/pith/ZR4OALQRNLSS66YN3HAVK66ZJ4","bundle":"https://pith.science/pith/ZR4OALQRNLSS66YN3HAVK66ZJ4/bundle.json","state":"https://pith.science/pith/ZR4OALQRNLSS66YN3HAVK66ZJ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZR4OALQRNLSS66YN3HAVK66ZJ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZR4OALQRNLSS66YN3HAVK66ZJ4","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":"de4b710c213ec79fa90d99604a1aa7be5eac418e09aad1cf561a09192a4790e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-04-29T13:35:06Z","title_canon_sha256":"56c7272427e236b2b8c581f754055b5de611f3d5bcad150ce8251525c6172253"},"schema_version":"1.0","source":{"id":"1504.07854","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07854","created_at":"2026-05-18T01:35:10Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07854v2","created_at":"2026-05-18T01:35:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07854","created_at":"2026-05-18T01:35:10Z"},{"alias_kind":"pith_short_12","alias_value":"ZR4OALQRNLSS","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZR4OALQRNLSS66YN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZR4OALQR","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:2266acff6b5a54f368a0cf30b6fe40e6d88a81cbb9f38e7cd31a3c779bbc9300","target":"graph","created_at":"2026-05-18T01:35:10Z","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":"We consider the motion of test particles in the spacetime of a black hole in f(R) gravity. The complete set of analytic solutions of the geodesic equation in the spacetime of this black hole are presented. The geodesic equations are solved in terms of Weierstrass elliptic functions and derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant $\\Lambda$ and the real constant $\\beta$.","authors_text":"Claus L\\\"ammerzahl, Jutta Kunz, Reza Saffari, Saheb Soroushfar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-04-29T13:35:06Z","title":"Analytical solutions of the geodesic equation in the spacetime of a black hole in f(R) gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07854","kind":"arxiv","version":2},"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:f7044d77e4a88c28110001c90f96dc04e41010e4d1b9045a08c8975ca59ae379","target":"record","created_at":"2026-05-18T01:35:10Z","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":"de4b710c213ec79fa90d99604a1aa7be5eac418e09aad1cf561a09192a4790e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-04-29T13:35:06Z","title_canon_sha256":"56c7272427e236b2b8c581f754055b5de611f3d5bcad150ce8251525c6172253"},"schema_version":"1.0","source":{"id":"1504.07854","kind":"arxiv","version":2}},"canonical_sha256":"cc78e02e116ae52f7b0dd9c1557bd94f08051f1040380b8cf6945b2e55055e4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc78e02e116ae52f7b0dd9c1557bd94f08051f1040380b8cf6945b2e55055e4d","first_computed_at":"2026-05-18T01:35:10.206249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:10.206249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6z//j86RMoU/oYvQnYtYD3snQOGeeYestzdXhYC1cn7jGsN9dUDxYB0LfXYaTlov8EsS9ywqILqvAyBmR0CODw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:10.206864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.07854","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7044d77e4a88c28110001c90f96dc04e41010e4d1b9045a08c8975ca59ae379","sha256:2266acff6b5a54f368a0cf30b6fe40e6d88a81cbb9f38e7cd31a3c779bbc9300"],"state_sha256":"34065ba46c835eb79930c4fd37d609a0b0a182ff3c9d3bad6edcea82f5024db8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SenRIRfVzhA3D0ZKKvcADfkpZrgqb6zvfSs1znpkjtW0CWfZQ2fUY3mMtMkR6RnC8S8mV9Ddh5a99YfYhjNfDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:11:01.124295Z","bundle_sha256":"6a3365de964be76228852f0ce3bfaf11206c8387bcaa62bb180ed175922f78db"}}