{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LLAUAJZFZLDYIYM4DHJJ4OCF3M","short_pith_number":"pith:LLAUAJZF","schema_version":"1.0","canonical_sha256":"5ac1402725cac784619c19d29e3845db0f6d0a1954e148b980f1afef7446b6d8","source":{"kind":"arxiv","id":"1803.09213","version":1},"attestation_state":"computed","paper":{"title":"Almost para-Hermitian and almost paracontact metric structures induced by natural Riemann extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Cornelia-Livia Bejan, Galia Nakova","submitted_at":"2018-03-25T08:29:57Z","abstract_excerpt":"In this paper we consider a manifold $(M,\\nabla )$ with a symmetric linear connection $\\nabla $ which induces on the cotangent bundle $T^*M$ of $M$ a semi-Riemannian metric $\\overline g$ with a neutral signature. The metric $\\overline g$ is called natural Riemann extension and it is a generalization (made by M. Sekizawa and O. Kowalski) of the Riemann extension, introduced by E. K. Patterson and A. G. Walker (1952). We construct two almost para-Hermitian structures on $(T^*M,\\overline g)$ which are almost para-K\\\"ahler or para-K\\\"ahler and prove that the defined almost para-complex structures "},"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":"1803.09213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-25T08:29:57Z","cross_cats_sorted":[],"title_canon_sha256":"c643d63eb37e1d1941d196f63e8e39533c0c5a29bc09f1ffa8c0ac87752881e7","abstract_canon_sha256":"e0f259624ab00b902ad37447b7deb12e4766d599078afa4025b2153bd6a83043"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:12.249640Z","signature_b64":"9peN/hww4n35QVNMbf9/teG3Fn+fdsJkoOQKDZDJqsImmd/J1+/SckcqbdCk4vB02bQhpS2nRKYyUw0S3ySkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ac1402725cac784619c19d29e3845db0f6d0a1954e148b980f1afef7446b6d8","last_reissued_at":"2026-05-18T00:20:12.248840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:12.248840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost para-Hermitian and almost paracontact metric structures induced by natural Riemann extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Cornelia-Livia Bejan, Galia Nakova","submitted_at":"2018-03-25T08:29:57Z","abstract_excerpt":"In this paper we consider a manifold $(M,\\nabla )$ with a symmetric linear connection $\\nabla $ which induces on the cotangent bundle $T^*M$ of $M$ a semi-Riemannian metric $\\overline g$ with a neutral signature. The metric $\\overline g$ is called natural Riemann extension and it is a generalization (made by M. Sekizawa and O. Kowalski) of the Riemann extension, introduced by E. K. Patterson and A. G. Walker (1952). We construct two almost para-Hermitian structures on $(T^*M,\\overline g)$ which are almost para-K\\\"ahler or para-K\\\"ahler and prove that the defined almost para-complex structures "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09213","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":"1803.09213","created_at":"2026-05-18T00:20:12.248979+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.09213v1","created_at":"2026-05-18T00:20:12.248979+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09213","created_at":"2026-05-18T00:20:12.248979+00:00"},{"alias_kind":"pith_short_12","alias_value":"LLAUAJZFZLDY","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LLAUAJZFZLDYIYM4","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LLAUAJZF","created_at":"2026-05-18T12:32:37.024351+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/LLAUAJZFZLDYIYM4DHJJ4OCF3M","json":"https://pith.science/pith/LLAUAJZFZLDYIYM4DHJJ4OCF3M.json","graph_json":"https://pith.science/api/pith-number/LLAUAJZFZLDYIYM4DHJJ4OCF3M/graph.json","events_json":"https://pith.science/api/pith-number/LLAUAJZFZLDYIYM4DHJJ4OCF3M/events.json","paper":"https://pith.science/paper/LLAUAJZF"},"agent_actions":{"view_html":"https://pith.science/pith/LLAUAJZFZLDYIYM4DHJJ4OCF3M","download_json":"https://pith.science/pith/LLAUAJZFZLDYIYM4DHJJ4OCF3M.json","view_paper":"https://pith.science/paper/LLAUAJZF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.09213&json=true","fetch_graph":"https://pith.science/api/pith-number/LLAUAJZFZLDYIYM4DHJJ4OCF3M/graph.json","fetch_events":"https://pith.science/api/pith-number/LLAUAJZFZLDYIYM4DHJJ4OCF3M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LLAUAJZFZLDYIYM4DHJJ4OCF3M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LLAUAJZFZLDYIYM4DHJJ4OCF3M/action/storage_attestation","attest_author":"https://pith.science/pith/LLAUAJZFZLDYIYM4DHJJ4OCF3M/action/author_attestation","sign_citation":"https://pith.science/pith/LLAUAJZFZLDYIYM4DHJJ4OCF3M/action/citation_signature","submit_replication":"https://pith.science/pith/LLAUAJZFZLDYIYM4DHJJ4OCF3M/action/replication_record"}},"created_at":"2026-05-18T00:20:12.248979+00:00","updated_at":"2026-05-18T00:20:12.248979+00:00"}