{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EY7RBT6J2TL73D5EO7Z4XP3TSU","short_pith_number":"pith:EY7RBT6J","canonical_record":{"source":{"id":"1803.02526","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2018-03-07T05:24:06Z","cross_cats_sorted":[],"title_canon_sha256":"e326530e9c848acaecfe5d5940967c22d506e097db5c086a243ebdb083f85aa4","abstract_canon_sha256":"bb9af87b21fc58e59374fa5effe68ef0839a7cf6ff08902df6b1e1c882072651"},"schema_version":"1.0"},"canonical_sha256":"263f10cfc9d4d7fd8fa477f3cbbf739527c6c7876b7488ad325f7ade50192daf","source":{"kind":"arxiv","id":"1803.02526","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02526","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02526v1","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02526","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"EY7RBT6J2TL7","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EY7RBT6J2TL73D5E","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EY7RBT6J","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EY7RBT6J2TL73D5EO7Z4XP3TSU","target":"record","payload":{"canonical_record":{"source":{"id":"1803.02526","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2018-03-07T05:24:06Z","cross_cats_sorted":[],"title_canon_sha256":"e326530e9c848acaecfe5d5940967c22d506e097db5c086a243ebdb083f85aa4","abstract_canon_sha256":"bb9af87b21fc58e59374fa5effe68ef0839a7cf6ff08902df6b1e1c882072651"},"schema_version":"1.0"},"canonical_sha256":"263f10cfc9d4d7fd8fa477f3cbbf739527c6c7876b7488ad325f7ade50192daf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:50.046258Z","signature_b64":"Lw4lAJ/ueBJySbA8RqvnY6pw9bbwmWcWfM32A2qgaZGvfZIE7hHWfVxPGoAtiv1fFffeHd924i0O2aSUqgjRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"263f10cfc9d4d7fd8fa477f3cbbf739527c6c7876b7488ad325f7ade50192daf","last_reissued_at":"2026-05-18T00:21:50.045802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:50.045802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.02526","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":"2026-05-18T00:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GtWFgqCNBM4U2vJw/Y5REp07omfWGXnd+iHjckpO+C8obusfe3IHBmcl7XXyGwMf95iR5vNOKtwlPYzHZ7u4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:22:37.440497Z"},"content_sha256":"4ff89f24d1fcfb4e203e58276405d770476e9a86a86c9cb69310c8771af2117e","schema_version":"1.0","event_id":"sha256:4ff89f24d1fcfb4e203e58276405d770476e9a86a86c9cb69310c8771af2117e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EY7RBT6J2TL73D5EO7Z4XP3TSU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of warped product submanifolds of Lorentzian concircular structure Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Laurian-Ioan Piscoran, Shyamal Kumar Hui, Tanumoy Pal","submitted_at":"2018-03-07T05:24:06Z","abstract_excerpt":"Recently Hui et al. (\\cite{HAP}, \\cite{HAN}) studied contact CR-warped product submanifolds and also warped product pseudo-slant submanifolds of a $(LCS)_n$-manifold $\\bar{M}$. In this paper we have studied the characterization for both these classes of warped product submanifolds. It is also shown that there do not exists any proper warped product bi-slant submanifold of a $(LCS)_n$-manifold. Although we constructed an example of a bi-slant submanifold of $(LCS)_n$-manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02526","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":"2026-05-18T00:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/XxDYYPPNOEUQQ3SJCbf2IalmY+DLW0sipDSUGUpnVXdXhEc91meoEGHCdjSx1zBlLj8xAh7J2WsnZyS+uVEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:22:37.440838Z"},"content_sha256":"a5fe35b5c9ec76a2687dbdb5294ecde6a528fe9893bf0acf369e1b5229790d78","schema_version":"1.0","event_id":"sha256:a5fe35b5c9ec76a2687dbdb5294ecde6a528fe9893bf0acf369e1b5229790d78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EY7RBT6J2TL73D5EO7Z4XP3TSU/bundle.json","state_url":"https://pith.science/pith/EY7RBT6J2TL73D5EO7Z4XP3TSU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EY7RBT6J2TL73D5EO7Z4XP3TSU/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":"2026-06-23T22:22:37Z","links":{"resolver":"https://pith.science/pith/EY7RBT6J2TL73D5EO7Z4XP3TSU","bundle":"https://pith.science/pith/EY7RBT6J2TL73D5EO7Z4XP3TSU/bundle.json","state":"https://pith.science/pith/EY7RBT6J2TL73D5EO7Z4XP3TSU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EY7RBT6J2TL73D5EO7Z4XP3TSU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EY7RBT6J2TL73D5EO7Z4XP3TSU","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":"bb9af87b21fc58e59374fa5effe68ef0839a7cf6ff08902df6b1e1c882072651","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2018-03-07T05:24:06Z","title_canon_sha256":"e326530e9c848acaecfe5d5940967c22d506e097db5c086a243ebdb083f85aa4"},"schema_version":"1.0","source":{"id":"1803.02526","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02526","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02526v1","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02526","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"EY7RBT6J2TL7","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EY7RBT6J2TL73D5E","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EY7RBT6J","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:a5fe35b5c9ec76a2687dbdb5294ecde6a528fe9893bf0acf369e1b5229790d78","target":"graph","created_at":"2026-05-18T00:21:50Z","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":"Recently Hui et al. (\\cite{HAP}, \\cite{HAN}) studied contact CR-warped product submanifolds and also warped product pseudo-slant submanifolds of a $(LCS)_n$-manifold $\\bar{M}$. In this paper we have studied the characterization for both these classes of warped product submanifolds. It is also shown that there do not exists any proper warped product bi-slant submanifold of a $(LCS)_n$-manifold. Although we constructed an example of a bi-slant submanifold of $(LCS)_n$-manifold.","authors_text":"Laurian-Ioan Piscoran, Shyamal Kumar Hui, Tanumoy Pal","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2018-03-07T05:24:06Z","title":"Characterization of warped product submanifolds of Lorentzian concircular structure Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02526","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":"sha256:4ff89f24d1fcfb4e203e58276405d770476e9a86a86c9cb69310c8771af2117e","target":"record","created_at":"2026-05-18T00:21:50Z","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":"bb9af87b21fc58e59374fa5effe68ef0839a7cf6ff08902df6b1e1c882072651","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2018-03-07T05:24:06Z","title_canon_sha256":"e326530e9c848acaecfe5d5940967c22d506e097db5c086a243ebdb083f85aa4"},"schema_version":"1.0","source":{"id":"1803.02526","kind":"arxiv","version":1}},"canonical_sha256":"263f10cfc9d4d7fd8fa477f3cbbf739527c6c7876b7488ad325f7ade50192daf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"263f10cfc9d4d7fd8fa477f3cbbf739527c6c7876b7488ad325f7ade50192daf","first_computed_at":"2026-05-18T00:21:50.045802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:50.045802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lw4lAJ/ueBJySbA8RqvnY6pw9bbwmWcWfM32A2qgaZGvfZIE7hHWfVxPGoAtiv1fFffeHd924i0O2aSUqgjRDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:50.046258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02526","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ff89f24d1fcfb4e203e58276405d770476e9a86a86c9cb69310c8771af2117e","sha256:a5fe35b5c9ec76a2687dbdb5294ecde6a528fe9893bf0acf369e1b5229790d78"],"state_sha256":"82147d73d8f1e2c787d1182d61896b25dd477e2a5c9509080b1a330c70ad6e86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BUgwGbeWAQH+mZ5UOnSyXxwylN1cpiUxDhJbbDeVNbQkKcByYKmtNyDGYWYx6k9Q3jYkbVPTdifXDBZcBENIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T22:22:37.442740Z","bundle_sha256":"57f72e1c21202a6b7425aa4337e768ee237b301c295aea23050470c92c728361"}}