{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:3CVJMP56JIHPHHACS6Q362V6KX","short_pith_number":"pith:3CVJMP56","canonical_record":{"source":{"id":"1906.01782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-06-05T02:00:59Z","cross_cats_sorted":[],"title_canon_sha256":"480c3edbd0b4599e3268b533dcd842725cf3c7ea00eaacf6b5d65e42ab02d097","abstract_canon_sha256":"5ac969829481a79b7f5a617170f3fec7ee2b1d4470f9db1725d67e0e11e0522a"},"schema_version":"1.0"},"canonical_sha256":"d8aa963fbe4a0ef39c0297a1bf6abe55cf5bdf9ddc7e2d2042fb8db6b33842f9","source":{"kind":"arxiv","id":"1906.01782","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01782","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01782v1","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01782","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"pith_short_12","alias_value":"3CVJMP56JIHP","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3CVJMP56JIHPHHAC","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3CVJMP56","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:3CVJMP56JIHPHHACS6Q362V6KX","target":"record","payload":{"canonical_record":{"source":{"id":"1906.01782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-06-05T02:00:59Z","cross_cats_sorted":[],"title_canon_sha256":"480c3edbd0b4599e3268b533dcd842725cf3c7ea00eaacf6b5d65e42ab02d097","abstract_canon_sha256":"5ac969829481a79b7f5a617170f3fec7ee2b1d4470f9db1725d67e0e11e0522a"},"schema_version":"1.0"},"canonical_sha256":"d8aa963fbe4a0ef39c0297a1bf6abe55cf5bdf9ddc7e2d2042fb8db6b33842f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:06.265601Z","signature_b64":"xCY+5Kw3HgTxgqBladJp5S57X5i/qrb9Te+RVsNB0dhnQc2mDNPn4onVc4sGawikb2N8wg0IWIwIE7jne69FAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8aa963fbe4a0ef39c0297a1bf6abe55cf5bdf9ddc7e2d2042fb8db6b33842f9","last_reissued_at":"2026-05-17T23:44:06.264996Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:06.264996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.01782","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":"2026-05-17T23:44:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LmVQ04muGGhf5I6uGmxAcWro1SQcjjwhMfvvFe3vGpmePLepRar+S1SPmGzuE19RPQyKHSFQChPIbXKQl/AGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:11:59.806096Z"},"content_sha256":"17c98763201ff5b8d43f48bbb2bbd3b6715b548592e32b0a08f37aee55614574","schema_version":"1.0","event_id":"sha256:17c98763201ff5b8d43f48bbb2bbd3b6715b548592e32b0a08f37aee55614574"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:3CVJMP56JIHPHHACS6Q362V6KX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Biharmonic hypersurfaces in a product space $L^m\\times \\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shun Maeta, Ye-Lin Ou, Yu Fu","submitted_at":"2019-06-05T02:00:59Z","abstract_excerpt":"In this paper, we study biharmonic hypersurfaces in a product of an Einstein space and a real line. We prove that a biharmonic hypersurface with constant mean curvature in such a product is either minimal or a vertical cylinder generalizing a result of \\cite{OW} and \\cite{FOR}. We derived the biharmonic equation for hypersurfaces in $S^m\\times \\mathbb{R}$ and $H^m\\times \\mathbb{R}$ in terms of the angle function of the hypersurface, and use it to obtain some classifications of biharmonic hypersurfaces in such spaces. These include classifications of biharmonic hypersurfaces which are totally u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01782","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":"2026-05-17T23:44:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E5XCm3Ov8hGOtm9JH5VI/72JOm/xnvniK59bAj+cqrMFLo/HbEZU7fsR3bonIQPMz9E4ssVBW0jmJWlpzQUvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:11:59.806743Z"},"content_sha256":"a13f4555afc6157ce3c7080f5fe8c6e8750302af611aacf964da164b1fb29d25","schema_version":"1.0","event_id":"sha256:a13f4555afc6157ce3c7080f5fe8c6e8750302af611aacf964da164b1fb29d25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3CVJMP56JIHPHHACS6Q362V6KX/bundle.json","state_url":"https://pith.science/pith/3CVJMP56JIHPHHACS6Q362V6KX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3CVJMP56JIHPHHACS6Q362V6KX/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":"2026-06-09T11:11:59Z","links":{"resolver":"https://pith.science/pith/3CVJMP56JIHPHHACS6Q362V6KX","bundle":"https://pith.science/pith/3CVJMP56JIHPHHACS6Q362V6KX/bundle.json","state":"https://pith.science/pith/3CVJMP56JIHPHHACS6Q362V6KX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3CVJMP56JIHPHHACS6Q362V6KX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3CVJMP56JIHPHHACS6Q362V6KX","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":"5ac969829481a79b7f5a617170f3fec7ee2b1d4470f9db1725d67e0e11e0522a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-06-05T02:00:59Z","title_canon_sha256":"480c3edbd0b4599e3268b533dcd842725cf3c7ea00eaacf6b5d65e42ab02d097"},"schema_version":"1.0","source":{"id":"1906.01782","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01782","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01782v1","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01782","created_at":"2026-05-17T23:44:06Z"},{"alias_kind":"pith_short_12","alias_value":"3CVJMP56JIHP","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3CVJMP56JIHPHHAC","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3CVJMP56","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:a13f4555afc6157ce3c7080f5fe8c6e8750302af611aacf964da164b1fb29d25","target":"graph","created_at":"2026-05-17T23:44:06Z","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 paper, we study biharmonic hypersurfaces in a product of an Einstein space and a real line. We prove that a biharmonic hypersurface with constant mean curvature in such a product is either minimal or a vertical cylinder generalizing a result of \\cite{OW} and \\cite{FOR}. We derived the biharmonic equation for hypersurfaces in $S^m\\times \\mathbb{R}$ and $H^m\\times \\mathbb{R}$ in terms of the angle function of the hypersurface, and use it to obtain some classifications of biharmonic hypersurfaces in such spaces. These include classifications of biharmonic hypersurfaces which are totally u","authors_text":"Shun Maeta, Ye-Lin Ou, Yu Fu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-06-05T02:00:59Z","title":"Biharmonic hypersurfaces in a product space $L^m\\times \\mathbb{R}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01782","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":"sha256:17c98763201ff5b8d43f48bbb2bbd3b6715b548592e32b0a08f37aee55614574","target":"record","created_at":"2026-05-17T23:44:06Z","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":"5ac969829481a79b7f5a617170f3fec7ee2b1d4470f9db1725d67e0e11e0522a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-06-05T02:00:59Z","title_canon_sha256":"480c3edbd0b4599e3268b533dcd842725cf3c7ea00eaacf6b5d65e42ab02d097"},"schema_version":"1.0","source":{"id":"1906.01782","kind":"arxiv","version":1}},"canonical_sha256":"d8aa963fbe4a0ef39c0297a1bf6abe55cf5bdf9ddc7e2d2042fb8db6b33842f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8aa963fbe4a0ef39c0297a1bf6abe55cf5bdf9ddc7e2d2042fb8db6b33842f9","first_computed_at":"2026-05-17T23:44:06.264996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:06.264996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xCY+5Kw3HgTxgqBladJp5S57X5i/qrb9Te+RVsNB0dhnQc2mDNPn4onVc4sGawikb2N8wg0IWIwIE7jne69FAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:06.265601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.01782","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17c98763201ff5b8d43f48bbb2bbd3b6715b548592e32b0a08f37aee55614574","sha256:a13f4555afc6157ce3c7080f5fe8c6e8750302af611aacf964da164b1fb29d25"],"state_sha256":"ad82df03d9df834e4bb540246cd13f9524d4fd982910cb780b75b9212753387d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oiGRbO3kKbcK9pfv4KfwHtJTTUK600PfY8BJh2JPfrsTdQdS35MTAt64qnc4O4sgiyAHMNooVY3qlNH52epxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:11:59.809582Z","bundle_sha256":"6eafae391dd7bdedd6d7f9479d7887ea9b319af199aa8b3adebb1dc103c70a8c"}}