{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:GKMGS7U6WHQ6EIAMZM4FPDDOB7","short_pith_number":"pith:GKMGS7U6","schema_version":"1.0","canonical_sha256":"3298697e9eb1e1e2200ccb38578c6e0fdd41a323207501cbf81f47cd9338d1ec","source":{"kind":"arxiv","id":"1012.2001","version":1},"attestation_state":"computed","paper":{"title":"Biharmonic Riemannian maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Bayram Sahin","submitted_at":"2010-12-09T13:39:38Z","abstract_excerpt":"We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that such Riemannian maps put some restrictions on the base manifolds."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.2001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-09T13:39:38Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0c944e00380a09cfa41bfe5a8647110ce663f189b6429c73784be4be6e919eee","abstract_canon_sha256":"873c8070d5f8f61ab50b1b36eb2dd5743f9ab20c079739e8140d9ff25c90a460"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:49.205725Z","signature_b64":"YCtfOerD5EAWXxx9DMUrbYiqNv++qXYaXQB+7ReWHph25ck3FOBidBVYEv/UMNu78vVA0RzsdOkpQThRDh1WCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3298697e9eb1e1e2200ccb38578c6e0fdd41a323207501cbf81f47cd9338d1ec","last_reissued_at":"2026-05-18T04:33:49.205089Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:49.205089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biharmonic Riemannian maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Bayram Sahin","submitted_at":"2010-12-09T13:39:38Z","abstract_excerpt":"We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that such Riemannian maps put some restrictions on the base manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2001","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.2001","created_at":"2026-05-18T04:33:49.205195+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.2001v1","created_at":"2026-05-18T04:33:49.205195+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2001","created_at":"2026-05-18T04:33:49.205195+00:00"},{"alias_kind":"pith_short_12","alias_value":"GKMGS7U6WHQ6","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"GKMGS7U6WHQ6EIAM","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"GKMGS7U6","created_at":"2026-05-18T12:26:07.630475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GKMGS7U6WHQ6EIAMZM4FPDDOB7","json":"https://pith.science/pith/GKMGS7U6WHQ6EIAMZM4FPDDOB7.json","graph_json":"https://pith.science/api/pith-number/GKMGS7U6WHQ6EIAMZM4FPDDOB7/graph.json","events_json":"https://pith.science/api/pith-number/GKMGS7U6WHQ6EIAMZM4FPDDOB7/events.json","paper":"https://pith.science/paper/GKMGS7U6"},"agent_actions":{"view_html":"https://pith.science/pith/GKMGS7U6WHQ6EIAMZM4FPDDOB7","download_json":"https://pith.science/pith/GKMGS7U6WHQ6EIAMZM4FPDDOB7.json","view_paper":"https://pith.science/paper/GKMGS7U6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.2001&json=true","fetch_graph":"https://pith.science/api/pith-number/GKMGS7U6WHQ6EIAMZM4FPDDOB7/graph.json","fetch_events":"https://pith.science/api/pith-number/GKMGS7U6WHQ6EIAMZM4FPDDOB7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GKMGS7U6WHQ6EIAMZM4FPDDOB7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GKMGS7U6WHQ6EIAMZM4FPDDOB7/action/storage_attestation","attest_author":"https://pith.science/pith/GKMGS7U6WHQ6EIAMZM4FPDDOB7/action/author_attestation","sign_citation":"https://pith.science/pith/GKMGS7U6WHQ6EIAMZM4FPDDOB7/action/citation_signature","submit_replication":"https://pith.science/pith/GKMGS7U6WHQ6EIAMZM4FPDDOB7/action/replication_record"}},"created_at":"2026-05-18T04:33:49.205195+00:00","updated_at":"2026-05-18T04:33:49.205195+00:00"}