{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:D4KAL52OF2R4VG4I2TETJGRNW4","short_pith_number":"pith:D4KAL52O","schema_version":"1.0","canonical_sha256":"1f1405f74e2ea3ca9b88d4c9349a2db72e0e441308029508470fc94705e8e01d","source":{"kind":"arxiv","id":"1801.05533","version":2},"attestation_state":"computed","paper":{"title":"Einstein-Weyl structures on almost cosymplectic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaomin Chen","submitted_at":"2018-01-17T03:05:51Z","abstract_excerpt":"In this article, we study Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic $(\\kappa,\\mu)$-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two Einstein-Weyl structures. Next for a three dimensional compact almost $\\alpha$-cosymplectic manifold admitting closed Einstein-Weyl structures, we prove that it is Ricc-flat. Further, we show that an almost $\\alpha$-cosymplectic admitting two Einstein-Weyl structures is either Einstein or $\\alpha$-cosymplectic, provided that its Ricci tensor is commuting. Finally, "},"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":"1801.05533","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-17T03:05:51Z","cross_cats_sorted":[],"title_canon_sha256":"f5be881a89c894117e79a120cf5de4d30feaaa593c5cb96f34e9a8b6cae42a99","abstract_canon_sha256":"d57be81941fd9750bd0ec420b0da0a4b14b24e53cbe90dcd2c757c83c058b6c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:08.846735Z","signature_b64":"ACzb3mz/JvOhOvbY62jaSiAY1ORF/ybKxPbc6HRfoZwo7m+br7ADT6qAkd/ZIPCtaTb017lbR/v9kYRvK/2wDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f1405f74e2ea3ca9b88d4c9349a2db72e0e441308029508470fc94705e8e01d","last_reissued_at":"2026-05-18T00:00:08.846259Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:08.846259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Einstein-Weyl structures on almost cosymplectic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaomin Chen","submitted_at":"2018-01-17T03:05:51Z","abstract_excerpt":"In this article, we study Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic $(\\kappa,\\mu)$-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two Einstein-Weyl structures. Next for a three dimensional compact almost $\\alpha$-cosymplectic manifold admitting closed Einstein-Weyl structures, we prove that it is Ricc-flat. Further, we show that an almost $\\alpha$-cosymplectic admitting two Einstein-Weyl structures is either Einstein or $\\alpha$-cosymplectic, provided that its Ricci tensor is commuting. Finally, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05533","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":"1801.05533","created_at":"2026-05-18T00:00:08.846355+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.05533v2","created_at":"2026-05-18T00:00:08.846355+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05533","created_at":"2026-05-18T00:00:08.846355+00:00"},{"alias_kind":"pith_short_12","alias_value":"D4KAL52OF2R4","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"D4KAL52OF2R4VG4I","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"D4KAL52O","created_at":"2026-05-18T12:32:19.392346+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/D4KAL52OF2R4VG4I2TETJGRNW4","json":"https://pith.science/pith/D4KAL52OF2R4VG4I2TETJGRNW4.json","graph_json":"https://pith.science/api/pith-number/D4KAL52OF2R4VG4I2TETJGRNW4/graph.json","events_json":"https://pith.science/api/pith-number/D4KAL52OF2R4VG4I2TETJGRNW4/events.json","paper":"https://pith.science/paper/D4KAL52O"},"agent_actions":{"view_html":"https://pith.science/pith/D4KAL52OF2R4VG4I2TETJGRNW4","download_json":"https://pith.science/pith/D4KAL52OF2R4VG4I2TETJGRNW4.json","view_paper":"https://pith.science/paper/D4KAL52O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.05533&json=true","fetch_graph":"https://pith.science/api/pith-number/D4KAL52OF2R4VG4I2TETJGRNW4/graph.json","fetch_events":"https://pith.science/api/pith-number/D4KAL52OF2R4VG4I2TETJGRNW4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D4KAL52OF2R4VG4I2TETJGRNW4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D4KAL52OF2R4VG4I2TETJGRNW4/action/storage_attestation","attest_author":"https://pith.science/pith/D4KAL52OF2R4VG4I2TETJGRNW4/action/author_attestation","sign_citation":"https://pith.science/pith/D4KAL52OF2R4VG4I2TETJGRNW4/action/citation_signature","submit_replication":"https://pith.science/pith/D4KAL52OF2R4VG4I2TETJGRNW4/action/replication_record"}},"created_at":"2026-05-18T00:00:08.846355+00:00","updated_at":"2026-05-18T00:00:08.846355+00:00"}