{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SL6YKAQPNVVCTXK4HFDGG6DR6F","short_pith_number":"pith:SL6YKAQP","schema_version":"1.0","canonical_sha256":"92fd85020f6d6a29dd5c3946637871f14060bd9f26c44a604d31329781c9ae25","source":{"kind":"arxiv","id":"1603.07058","version":3},"attestation_state":"computed","paper":{"title":"On Bismut Flat Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bo Yang, Fangyang Zheng, Qingsong Wang","submitted_at":"2016-03-23T03:14:17Z","abstract_excerpt":"In this paper, we give a classification of all compact Hermitian manifolds with flat Bismut connection. We show that the torsion tensor of such a manifold must be parallel, thus the universal cover of such a manifold is a Lie group equipped with a bi-invariant metric and a compatible left invariant complex structure. In particular, isosceles Hopf surfaces are the only Bismut flat compact non-K\\\"ahler surfaces, while central Calabi-Eckmann threefolds are the only simply-connected compact Bismut flat threefolds."},"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":"1603.07058","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-23T03:14:17Z","cross_cats_sorted":[],"title_canon_sha256":"88aca4cebefe09432ed9939fef9e1a493a32cb95af00246c42c70fd0af075bb6","abstract_canon_sha256":"113ff10d71b652583efec077ca3716ae7240447b3ca4c2f6770f4920fd127761"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:56:11.840124Z","signature_b64":"MMh+2jf1hijhG3Q2GDVrkzwFayK0nqA68WlMDP0Keqi2gZbZR+YOlNOQ5IxwzFku4nQ+oxZH4wx2FTRSHEimCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92fd85020f6d6a29dd5c3946637871f14060bd9f26c44a604d31329781c9ae25","last_reissued_at":"2026-07-05T05:56:11.839690Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:56:11.839690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Bismut Flat Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bo Yang, Fangyang Zheng, Qingsong Wang","submitted_at":"2016-03-23T03:14:17Z","abstract_excerpt":"In this paper, we give a classification of all compact Hermitian manifolds with flat Bismut connection. We show that the torsion tensor of such a manifold must be parallel, thus the universal cover of such a manifold is a Lie group equipped with a bi-invariant metric and a compatible left invariant complex structure. In particular, isosceles Hopf surfaces are the only Bismut flat compact non-K\\\"ahler surfaces, while central Calabi-Eckmann threefolds are the only simply-connected compact Bismut flat threefolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07058","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1603.07058/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1603.07058","created_at":"2026-07-05T05:56:11.839757+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.07058v3","created_at":"2026-07-05T05:56:11.839757+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07058","created_at":"2026-07-05T05:56:11.839757+00:00"},{"alias_kind":"pith_short_12","alias_value":"SL6YKAQPNVVC","created_at":"2026-07-05T05:56:11.839757+00:00"},{"alias_kind":"pith_short_16","alias_value":"SL6YKAQPNVVCTXK4","created_at":"2026-07-05T05:56:11.839757+00:00"},{"alias_kind":"pith_short_8","alias_value":"SL6YKAQP","created_at":"2026-07-05T05:56:11.839757+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.05322","citing_title":"On Strominger K\\\"ahler-like manifolds with degenerate torsion","ref_index":41,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SL6YKAQPNVVCTXK4HFDGG6DR6F","json":"https://pith.science/pith/SL6YKAQPNVVCTXK4HFDGG6DR6F.json","graph_json":"https://pith.science/api/pith-number/SL6YKAQPNVVCTXK4HFDGG6DR6F/graph.json","events_json":"https://pith.science/api/pith-number/SL6YKAQPNVVCTXK4HFDGG6DR6F/events.json","paper":"https://pith.science/paper/SL6YKAQP"},"agent_actions":{"view_html":"https://pith.science/pith/SL6YKAQPNVVCTXK4HFDGG6DR6F","download_json":"https://pith.science/pith/SL6YKAQPNVVCTXK4HFDGG6DR6F.json","view_paper":"https://pith.science/paper/SL6YKAQP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.07058&json=true","fetch_graph":"https://pith.science/api/pith-number/SL6YKAQPNVVCTXK4HFDGG6DR6F/graph.json","fetch_events":"https://pith.science/api/pith-number/SL6YKAQPNVVCTXK4HFDGG6DR6F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SL6YKAQPNVVCTXK4HFDGG6DR6F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SL6YKAQPNVVCTXK4HFDGG6DR6F/action/storage_attestation","attest_author":"https://pith.science/pith/SL6YKAQPNVVCTXK4HFDGG6DR6F/action/author_attestation","sign_citation":"https://pith.science/pith/SL6YKAQPNVVCTXK4HFDGG6DR6F/action/citation_signature","submit_replication":"https://pith.science/pith/SL6YKAQPNVVCTXK4HFDGG6DR6F/action/replication_record"}},"created_at":"2026-07-05T05:56:11.839757+00:00","updated_at":"2026-07-05T05:56:11.839757+00:00"}