{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BD77MMTNYVSFA2WRAM6O26LBWB","short_pith_number":"pith:BD77MMTN","canonical_record":{"source":{"id":"1510.02016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-10-07T16:33:09Z","cross_cats_sorted":[],"title_canon_sha256":"81e090bd012c9465a26db0d2f6b00e5230e2689f9f29563f718b52f875689e45","abstract_canon_sha256":"2490ba36b71d94a604aac75d5734bafe0b239a7eccbbb56bc9a15db9fd0cfdef"},"schema_version":"1.0"},"canonical_sha256":"08fff6326dc564506ad1033ced7961b053ea61aeff94b13fcaf73126d6407bd9","source":{"kind":"arxiv","id":"1510.02016","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02016","created_at":"2026-05-18T01:21:30Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02016v1","created_at":"2026-05-18T01:21:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02016","created_at":"2026-05-18T01:21:30Z"},{"alias_kind":"pith_short_12","alias_value":"BD77MMTNYVSF","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BD77MMTNYVSFA2WR","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BD77MMTN","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BD77MMTNYVSFA2WRAM6O26LBWB","target":"record","payload":{"canonical_record":{"source":{"id":"1510.02016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-10-07T16:33:09Z","cross_cats_sorted":[],"title_canon_sha256":"81e090bd012c9465a26db0d2f6b00e5230e2689f9f29563f718b52f875689e45","abstract_canon_sha256":"2490ba36b71d94a604aac75d5734bafe0b239a7eccbbb56bc9a15db9fd0cfdef"},"schema_version":"1.0"},"canonical_sha256":"08fff6326dc564506ad1033ced7961b053ea61aeff94b13fcaf73126d6407bd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:30.699028Z","signature_b64":"q6B/oHJAYWdWYADJqJU33bOjIpZJq7/gZLA64X5psf4JcX4VOvIK7Fc2OVmjwQcpZyLcgsx1aOsEgOs9y6tsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08fff6326dc564506ad1033ced7961b053ea61aeff94b13fcaf73126d6407bd9","last_reissued_at":"2026-05-18T01:21:30.698381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:30.698381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.02016","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":"2026-05-18T01:21:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OT9OcBOuyn6CZFT7nlFXekDfCFe7OD4xg7yzFvCbfcyTk49bRK97TjFFWrZuP+7kFzZFyQG31vT1+5u1rYJMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:43:44.061344Z"},"content_sha256":"d03a48c8cd3efe062c9091f10ff1389c25cec693e64d54790b685b4c17c604b6","schema_version":"1.0","event_id":"sha256:d03a48c8cd3efe062c9091f10ff1389c25cec693e64d54790b685b4c17c604b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BD77MMTNYVSFA2WRAM6O26LBWB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geodesics in the field of a rotating deformed gravitational source","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Hernando Quevedo, Kuantay Boshkayev, Marzhan Abutalip, Sharara Suleymanova, Zhanerke Kalymova","submitted_at":"2015-10-07T16:33:09Z","abstract_excerpt":"We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the sourc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02016","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":"2026-05-18T01:21:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nmFb6Z8n9EN19rp+Rc2YJi3JlQxmvE2I/F/vJAxCFR20KTYc6qvLuEBAziT6y+QJJVBJVl597VZFZKbR6d/zAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:43:44.061698Z"},"content_sha256":"9b465bf16c888e0cf1d5cdfcf9e83b26ddb65684eb5d126185d60eb496fd6a7c","schema_version":"1.0","event_id":"sha256:9b465bf16c888e0cf1d5cdfcf9e83b26ddb65684eb5d126185d60eb496fd6a7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BD77MMTNYVSFA2WRAM6O26LBWB/bundle.json","state_url":"https://pith.science/pith/BD77MMTNYVSFA2WRAM6O26LBWB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BD77MMTNYVSFA2WRAM6O26LBWB/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":"2026-05-28T20:43:44Z","links":{"resolver":"https://pith.science/pith/BD77MMTNYVSFA2WRAM6O26LBWB","bundle":"https://pith.science/pith/BD77MMTNYVSFA2WRAM6O26LBWB/bundle.json","state":"https://pith.science/pith/BD77MMTNYVSFA2WRAM6O26LBWB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BD77MMTNYVSFA2WRAM6O26LBWB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BD77MMTNYVSFA2WRAM6O26LBWB","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":"2490ba36b71d94a604aac75d5734bafe0b239a7eccbbb56bc9a15db9fd0cfdef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-10-07T16:33:09Z","title_canon_sha256":"81e090bd012c9465a26db0d2f6b00e5230e2689f9f29563f718b52f875689e45"},"schema_version":"1.0","source":{"id":"1510.02016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02016","created_at":"2026-05-18T01:21:30Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02016v1","created_at":"2026-05-18T01:21:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02016","created_at":"2026-05-18T01:21:30Z"},{"alias_kind":"pith_short_12","alias_value":"BD77MMTNYVSF","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BD77MMTNYVSFA2WR","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BD77MMTN","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:9b465bf16c888e0cf1d5cdfcf9e83b26ddb65684eb5d126185d60eb496fd6a7c","target":"graph","created_at":"2026-05-18T01:21:30Z","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 investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic expressions for the orbital angular velocity, the specific angular momentum and energy, and the radii of marginally stable and marginally bound circular orbits. Moreover, we calculate the orbital angular velocity and the radius of lightlike circular geodesics. We study numerically the frame dragging effect and the influence of the quadrupolar deformation of the sourc","authors_text":"Hernando Quevedo, Kuantay Boshkayev, Marzhan Abutalip, Sharara Suleymanova, Zhanerke Kalymova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-10-07T16:33:09Z","title":"Geodesics in the field of a rotating deformed gravitational source"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02016","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:d03a48c8cd3efe062c9091f10ff1389c25cec693e64d54790b685b4c17c604b6","target":"record","created_at":"2026-05-18T01:21:30Z","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":"2490ba36b71d94a604aac75d5734bafe0b239a7eccbbb56bc9a15db9fd0cfdef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-10-07T16:33:09Z","title_canon_sha256":"81e090bd012c9465a26db0d2f6b00e5230e2689f9f29563f718b52f875689e45"},"schema_version":"1.0","source":{"id":"1510.02016","kind":"arxiv","version":1}},"canonical_sha256":"08fff6326dc564506ad1033ced7961b053ea61aeff94b13fcaf73126d6407bd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08fff6326dc564506ad1033ced7961b053ea61aeff94b13fcaf73126d6407bd9","first_computed_at":"2026-05-18T01:21:30.698381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:30.698381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q6B/oHJAYWdWYADJqJU33bOjIpZJq7/gZLA64X5psf4JcX4VOvIK7Fc2OVmjwQcpZyLcgsx1aOsEgOs9y6tsCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:30.699028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.02016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d03a48c8cd3efe062c9091f10ff1389c25cec693e64d54790b685b4c17c604b6","sha256:9b465bf16c888e0cf1d5cdfcf9e83b26ddb65684eb5d126185d60eb496fd6a7c"],"state_sha256":"8bdd5dc6cb1a0d88c26a1b66cbd9f412e0842c28753eb2e03c294ade7291d04a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vuqp2lRSC3LsduoHaBWDWUe5smxqqu8Hu+MmQJEjKfA+AuEhzljLjBiJYeaUUtd2DFCwmbyFFSdk9v+ULG4vDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:43:44.063999Z","bundle_sha256":"b59f32315f58ea9e065b7b489e714ce34a4bc03dc12b1d63011b8011f12ba2c3"}}