{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:H5XWNX5INUV5XTMLBQ7BMLTWCQ","short_pith_number":"pith:H5XWNX5I","schema_version":"1.0","canonical_sha256":"3f6f66dfa86d2bdbcd8b0c3e162e76140567675283f3113e0ef282b3ac08a092","source":{"kind":"arxiv","id":"1810.00772","version":2},"attestation_state":"computed","paper":{"title":"Sasakian immersions into the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrea Loi, Beniamino Cappelletti-Montano","submitted_at":"2018-10-01T15:48:49Z","abstract_excerpt":"The aim of this paper is to study Sasakian immersions of compact Sasakian manifolds into the odd-dimensional sphere equipped with the standard Sasakian structure. We obtain a complete classification of such manifolds in the Einstein and $\\eta$-Einstein cases when the codimension of the immersion is $4$. Moreover, we exhibit infinite families of compact Sasakian $\\eta$--Einstein manifolds which cannot admit a Sasakian immersion into any odd-dimensional sphere. Finally, we show that, after possibly performing a ${\\mathcal {D}}$-homothetic deformation, a homogeneous Sasakian manifold can be Sasak"},"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":"1810.00772","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-01T15:48:49Z","cross_cats_sorted":[],"title_canon_sha256":"5081dbb3799ddee1325978b6431e9feaaf3d12c976e97e9da31a296eb5ed24de","abstract_canon_sha256":"7e403c7d61f5db75685a0125672b62118cf00e0133efc73635a458a4fbd9a4a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:59.343051Z","signature_b64":"+LP7J2jiR1KUG/5xJL74Xrd7veCLtkIu4u4qlpBR5W/Ycboscees+Ek6yLondDDg6KNXYexJe6l/WQK6jBWzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f6f66dfa86d2bdbcd8b0c3e162e76140567675283f3113e0ef282b3ac08a092","last_reissued_at":"2026-05-18T00:02:59.342344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:59.342344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sasakian immersions into the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrea Loi, Beniamino Cappelletti-Montano","submitted_at":"2018-10-01T15:48:49Z","abstract_excerpt":"The aim of this paper is to study Sasakian immersions of compact Sasakian manifolds into the odd-dimensional sphere equipped with the standard Sasakian structure. We obtain a complete classification of such manifolds in the Einstein and $\\eta$-Einstein cases when the codimension of the immersion is $4$. Moreover, we exhibit infinite families of compact Sasakian $\\eta$--Einstein manifolds which cannot admit a Sasakian immersion into any odd-dimensional sphere. Finally, we show that, after possibly performing a ${\\mathcal {D}}$-homothetic deformation, a homogeneous Sasakian manifold can be Sasak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00772","kind":"arxiv","version":2},"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":"1810.00772","created_at":"2026-05-18T00:02:59.342469+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.00772v2","created_at":"2026-05-18T00:02:59.342469+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00772","created_at":"2026-05-18T00:02:59.342469+00:00"},{"alias_kind":"pith_short_12","alias_value":"H5XWNX5INUV5","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"H5XWNX5INUV5XTML","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"H5XWNX5I","created_at":"2026-05-18T12:32:28.185984+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/H5XWNX5INUV5XTMLBQ7BMLTWCQ","json":"https://pith.science/pith/H5XWNX5INUV5XTMLBQ7BMLTWCQ.json","graph_json":"https://pith.science/api/pith-number/H5XWNX5INUV5XTMLBQ7BMLTWCQ/graph.json","events_json":"https://pith.science/api/pith-number/H5XWNX5INUV5XTMLBQ7BMLTWCQ/events.json","paper":"https://pith.science/paper/H5XWNX5I"},"agent_actions":{"view_html":"https://pith.science/pith/H5XWNX5INUV5XTMLBQ7BMLTWCQ","download_json":"https://pith.science/pith/H5XWNX5INUV5XTMLBQ7BMLTWCQ.json","view_paper":"https://pith.science/paper/H5XWNX5I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.00772&json=true","fetch_graph":"https://pith.science/api/pith-number/H5XWNX5INUV5XTMLBQ7BMLTWCQ/graph.json","fetch_events":"https://pith.science/api/pith-number/H5XWNX5INUV5XTMLBQ7BMLTWCQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H5XWNX5INUV5XTMLBQ7BMLTWCQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H5XWNX5INUV5XTMLBQ7BMLTWCQ/action/storage_attestation","attest_author":"https://pith.science/pith/H5XWNX5INUV5XTMLBQ7BMLTWCQ/action/author_attestation","sign_citation":"https://pith.science/pith/H5XWNX5INUV5XTMLBQ7BMLTWCQ/action/citation_signature","submit_replication":"https://pith.science/pith/H5XWNX5INUV5XTMLBQ7BMLTWCQ/action/replication_record"}},"created_at":"2026-05-18T00:02:59.342469+00:00","updated_at":"2026-05-18T00:02:59.342469+00:00"}