{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:47OBNRSR44DGDFSK6JNMHLCO37","short_pith_number":"pith:47OBNRSR","canonical_record":{"source":{"id":"1508.03444","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-14T09:10:52Z","cross_cats_sorted":[],"title_canon_sha256":"b0e6d433fd9e4e7a0f389a932ddfee7ce956d23e7c609208862c0ee2b839a885","abstract_canon_sha256":"04f23c0aeac15199f36c3c5bcca1cf86ce279151e41d6e062471c0e1cb10a2f8"},"schema_version":"1.0"},"canonical_sha256":"e7dc16c651e70661964af25ac3ac4edfe3a04a4857b8c56d63dbe29c1a5e354a","source":{"kind":"arxiv","id":"1508.03444","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03444","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03444v2","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03444","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"47OBNRSR44DG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"47OBNRSR44DGDFSK","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"47OBNRSR","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:47OBNRSR44DGDFSK6JNMHLCO37","target":"record","payload":{"canonical_record":{"source":{"id":"1508.03444","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-14T09:10:52Z","cross_cats_sorted":[],"title_canon_sha256":"b0e6d433fd9e4e7a0f389a932ddfee7ce956d23e7c609208862c0ee2b839a885","abstract_canon_sha256":"04f23c0aeac15199f36c3c5bcca1cf86ce279151e41d6e062471c0e1cb10a2f8"},"schema_version":"1.0"},"canonical_sha256":"e7dc16c651e70661964af25ac3ac4edfe3a04a4857b8c56d63dbe29c1a5e354a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:51.575461Z","signature_b64":"N/6C3puqdPhD378Q7GjCz0xIaDl+OPMVafWnCXNPU95qLA8kpnWzlpCaMn93LQw0TcAJXXc+KRzVkciJTaCQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7dc16c651e70661964af25ac3ac4edfe3a04a4857b8c56d63dbe29c1a5e354a","last_reissued_at":"2026-05-18T00:41:51.575005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:51.575005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.03444","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":"2026-05-18T00:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e9lBxBlrgAYaFtVNsYTlT47HWjrHeFaBAurmJ839GiOiyTyJZjsso8IEgdru7paXpUu6aWv3/476PK5f0ZisDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:01:24.101955Z"},"content_sha256":"aac441b4f0dd5421eb33f3799eae6b2a16efd12c524fecdeec94832fb7508afa","schema_version":"1.0","event_id":"sha256:aac441b4f0dd5421eb33f3799eae6b2a16efd12c524fecdeec94832fb7508afa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:47OBNRSR44DGDFSK6JNMHLCO37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conformal vector fields on doubly warped product manifolds and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"H. K. El-Sayied, Noha Syied, Sameh Shenawy","submitted_at":"2015-08-14T09:10:52Z","abstract_excerpt":"In this article, we present a complete study of two disjoint classes of conformal vector fields on doubly warped product manifolds as well as on doubly warped space-times. Then we study Ricci solitons on doubly warped product manifollds admitting these types of conformal vector fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03444","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":"2026-05-18T00:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0UsS+MDBgOqzUeYPPoB1HJ0KOMFaYbBiQ1H3Mzm20p36mI10yENN9sNF2K20GuCq0P2ScOZwN9gzWB0QVRKxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:01:24.102337Z"},"content_sha256":"1969ffeedc2c734f070b07e78aabcf0ef3a018dbb7121e4d6718c4c355f3b512","schema_version":"1.0","event_id":"sha256:1969ffeedc2c734f070b07e78aabcf0ef3a018dbb7121e4d6718c4c355f3b512"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/47OBNRSR44DGDFSK6JNMHLCO37/bundle.json","state_url":"https://pith.science/pith/47OBNRSR44DGDFSK6JNMHLCO37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/47OBNRSR44DGDFSK6JNMHLCO37/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":"2026-06-20T10:01:24Z","links":{"resolver":"https://pith.science/pith/47OBNRSR44DGDFSK6JNMHLCO37","bundle":"https://pith.science/pith/47OBNRSR44DGDFSK6JNMHLCO37/bundle.json","state":"https://pith.science/pith/47OBNRSR44DGDFSK6JNMHLCO37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/47OBNRSR44DGDFSK6JNMHLCO37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:47OBNRSR44DGDFSK6JNMHLCO37","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":"04f23c0aeac15199f36c3c5bcca1cf86ce279151e41d6e062471c0e1cb10a2f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-14T09:10:52Z","title_canon_sha256":"b0e6d433fd9e4e7a0f389a932ddfee7ce956d23e7c609208862c0ee2b839a885"},"schema_version":"1.0","source":{"id":"1508.03444","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03444","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03444v2","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03444","created_at":"2026-05-18T00:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"47OBNRSR44DG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"47OBNRSR44DGDFSK","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"47OBNRSR","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:1969ffeedc2c734f070b07e78aabcf0ef3a018dbb7121e4d6718c4c355f3b512","target":"graph","created_at":"2026-05-18T00:41:51Z","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":"In this article, we present a complete study of two disjoint classes of conformal vector fields on doubly warped product manifolds as well as on doubly warped space-times. Then we study Ricci solitons on doubly warped product manifollds admitting these types of conformal vector fields.","authors_text":"H. K. El-Sayied, Noha Syied, Sameh Shenawy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-14T09:10:52Z","title":"Conformal vector fields on doubly warped product manifolds and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03444","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:aac441b4f0dd5421eb33f3799eae6b2a16efd12c524fecdeec94832fb7508afa","target":"record","created_at":"2026-05-18T00:41:51Z","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":"04f23c0aeac15199f36c3c5bcca1cf86ce279151e41d6e062471c0e1cb10a2f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-14T09:10:52Z","title_canon_sha256":"b0e6d433fd9e4e7a0f389a932ddfee7ce956d23e7c609208862c0ee2b839a885"},"schema_version":"1.0","source":{"id":"1508.03444","kind":"arxiv","version":2}},"canonical_sha256":"e7dc16c651e70661964af25ac3ac4edfe3a04a4857b8c56d63dbe29c1a5e354a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7dc16c651e70661964af25ac3ac4edfe3a04a4857b8c56d63dbe29c1a5e354a","first_computed_at":"2026-05-18T00:41:51.575005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:51.575005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N/6C3puqdPhD378Q7GjCz0xIaDl+OPMVafWnCXNPU95qLA8kpnWzlpCaMn93LQw0TcAJXXc+KRzVkciJTaCQBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:51.575461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03444","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aac441b4f0dd5421eb33f3799eae6b2a16efd12c524fecdeec94832fb7508afa","sha256:1969ffeedc2c734f070b07e78aabcf0ef3a018dbb7121e4d6718c4c355f3b512"],"state_sha256":"013f41d91eea6bc87a2e0ce95de78562c8f33ba94e085b01b3ac99c13ffbf686"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2R0Rfwu/Fax2nVOlKYeb+exnmTMjhBBVN4Pw5albU5k8VIflH56L4lt126MDh5Da5daXyI3sDYjksA9HJKL7CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T10:01:24.104328Z","bundle_sha256":"1e8d4fccb35a98847a552c8ebff366504a6efe47d9da908e25fd79bf079032b5"}}