{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:N575Y7NTZPEJSHQ3IMAXZFKRPS","short_pith_number":"pith:N575Y7NT","canonical_record":{"source":{"id":"1905.02006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-02T18:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"8da00d65f2ae0b45c1a64a205e6450f90f4872d20f4ac130cd82810886c72369","abstract_canon_sha256":"6413319198e7f3e0d00c637abd2bbf0ea65e9789c4ee488099d47fa0ef67eaf7"},"schema_version":"1.0"},"canonical_sha256":"6f7fdc7db3cbc8991e1b43017c95517c9f7ca1017eb00f807fce9e6e59e94d2f","source":{"kind":"arxiv","id":"1905.02006","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02006","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02006v1","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02006","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"pith_short_12","alias_value":"N575Y7NTZPEJ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N575Y7NTZPEJSHQ3","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N575Y7NT","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:N575Y7NTZPEJSHQ3IMAXZFKRPS","target":"record","payload":{"canonical_record":{"source":{"id":"1905.02006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-02T18:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"8da00d65f2ae0b45c1a64a205e6450f90f4872d20f4ac130cd82810886c72369","abstract_canon_sha256":"6413319198e7f3e0d00c637abd2bbf0ea65e9789c4ee488099d47fa0ef67eaf7"},"schema_version":"1.0"},"canonical_sha256":"6f7fdc7db3cbc8991e1b43017c95517c9f7ca1017eb00f807fce9e6e59e94d2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:56.710838Z","signature_b64":"j9uq9hUfkByOP9ahtsQ4v4n7TSjxZ1nJNqtmbVstjE0jCDLe6B2m6OBd7aLkWp5M8DsMNM8aeWJwbqVAqfyaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f7fdc7db3cbc8991e1b43017c95517c9f7ca1017eb00f807fce9e6e59e94d2f","last_reissued_at":"2026-05-17T23:46:56.710148Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:56.710148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.02006","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":"2026-05-17T23:46:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XDhU/bwvJ9kejISM4vLUp/kc7W+eZ09EkrSy0Fr1C/gVCpvj08vHT/MgNLryVbZxHZIxepbaBCygpAI0f3qICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T01:49:05.845169Z"},"content_sha256":"b42306745db8773fe7a90ee3952fa2ffce9ec4c81fee3c46018f924df0dd03db","schema_version":"1.0","event_id":"sha256:b42306745db8773fe7a90ee3952fa2ffce9ec4c81fee3c46018f924df0dd03db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:N575Y7NTZPEJSHQ3IMAXZFKRPS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-Einstein manifolds with structure of warped product product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Paula Gon\\c{c}alves Correia Bonfim, Romildo Pina","submitted_at":"2019-05-02T18:29:17Z","abstract_excerpt":"In this paper we prove that under certain conditions in a quasi Einstein semi Riemannian warped product the fiber is necessarily a Einstein manifold. We provide all the quasi Einstein manifolds when r Bakry Emery tensor is null, the base is conformal to an n-dimensional pseudo-Euclidean space invariant under the action of an n - 1 dimensional translation group and the fiber is Ricci flat. As an application, we have built a family of Ricci flat Einstein warped product whose base is not locally conformally flat."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02006","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":"2026-05-17T23:46:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GDpcTXp+6wDIQbt7g7eGGxTvbs9tlA2pbvxfSAILMt2tfmFLg2bseUyHwZHQJ3tUFD0H4qsZuUoQUjHo0WuoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T01:49:05.845536Z"},"content_sha256":"7bcc02ce19cf602901112107677867b5949505f0f35c7891200be736cac27c2c","schema_version":"1.0","event_id":"sha256:7bcc02ce19cf602901112107677867b5949505f0f35c7891200be736cac27c2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N575Y7NTZPEJSHQ3IMAXZFKRPS/bundle.json","state_url":"https://pith.science/pith/N575Y7NTZPEJSHQ3IMAXZFKRPS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N575Y7NTZPEJSHQ3IMAXZFKRPS/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":"2026-06-24T01:49:05Z","links":{"resolver":"https://pith.science/pith/N575Y7NTZPEJSHQ3IMAXZFKRPS","bundle":"https://pith.science/pith/N575Y7NTZPEJSHQ3IMAXZFKRPS/bundle.json","state":"https://pith.science/pith/N575Y7NTZPEJSHQ3IMAXZFKRPS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N575Y7NTZPEJSHQ3IMAXZFKRPS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:N575Y7NTZPEJSHQ3IMAXZFKRPS","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":"6413319198e7f3e0d00c637abd2bbf0ea65e9789c4ee488099d47fa0ef67eaf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-02T18:29:17Z","title_canon_sha256":"8da00d65f2ae0b45c1a64a205e6450f90f4872d20f4ac130cd82810886c72369"},"schema_version":"1.0","source":{"id":"1905.02006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02006","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02006v1","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02006","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"pith_short_12","alias_value":"N575Y7NTZPEJ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N575Y7NTZPEJSHQ3","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N575Y7NT","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:7bcc02ce19cf602901112107677867b5949505f0f35c7891200be736cac27c2c","target":"graph","created_at":"2026-05-17T23:46:56Z","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 prove that under certain conditions in a quasi Einstein semi Riemannian warped product the fiber is necessarily a Einstein manifold. We provide all the quasi Einstein manifolds when r Bakry Emery tensor is null, the base is conformal to an n-dimensional pseudo-Euclidean space invariant under the action of an n - 1 dimensional translation group and the fiber is Ricci flat. As an application, we have built a family of Ricci flat Einstein warped product whose base is not locally conformally flat.","authors_text":"Paula Gon\\c{c}alves Correia Bonfim, Romildo Pina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-02T18:29:17Z","title":"Quasi-Einstein manifolds with structure of warped product product"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02006","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:b42306745db8773fe7a90ee3952fa2ffce9ec4c81fee3c46018f924df0dd03db","target":"record","created_at":"2026-05-17T23:46:56Z","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":"6413319198e7f3e0d00c637abd2bbf0ea65e9789c4ee488099d47fa0ef67eaf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-05-02T18:29:17Z","title_canon_sha256":"8da00d65f2ae0b45c1a64a205e6450f90f4872d20f4ac130cd82810886c72369"},"schema_version":"1.0","source":{"id":"1905.02006","kind":"arxiv","version":1}},"canonical_sha256":"6f7fdc7db3cbc8991e1b43017c95517c9f7ca1017eb00f807fce9e6e59e94d2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f7fdc7db3cbc8991e1b43017c95517c9f7ca1017eb00f807fce9e6e59e94d2f","first_computed_at":"2026-05-17T23:46:56.710148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:56.710148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j9uq9hUfkByOP9ahtsQ4v4n7TSjxZ1nJNqtmbVstjE0jCDLe6B2m6OBd7aLkWp5M8DsMNM8aeWJwbqVAqfyaDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:56.710838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.02006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b42306745db8773fe7a90ee3952fa2ffce9ec4c81fee3c46018f924df0dd03db","sha256:7bcc02ce19cf602901112107677867b5949505f0f35c7891200be736cac27c2c"],"state_sha256":"d90063eabc53ff168c109f7ca99974ab23ed7dd3d1c84460cec4adec18a4a119"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3LCG4X1YXkjZigsg1qJlJ3t/TqKwqvAiGWByxRWAX12ikL6GXD6A/hjKOgx/7cWfgANcuebgonptO867Hw+oDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T01:49:05.847566Z","bundle_sha256":"9185c0ca5e4a8f49c0acfddbb5fd01b10d3778e0480657570729c185bce840c5"}}