{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:OH43VCXOMIAVVCQTUM5EA3L7RK","short_pith_number":"pith:OH43VCXO","schema_version":"1.0","canonical_sha256":"71f9ba8aee62015a8a13a33a406d7f8a92cf409eefb0cd2582c19539c9ef9bbb","source":{"kind":"arxiv","id":"2307.10207","version":2},"attestation_state":"computed","paper":{"title":"Bismut Hermitian Einstein metrics and the stability of the pluriclosed flow","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Giuseppe Barbaro","submitted_at":"2023-07-14T10:09:01Z","abstract_excerpt":"We compute the (1,1)-Aeppli cohomology of compact simply-connected Lie groups. From this, we deduce that the Bismut flat metrics on the compact Bismut flat manifolds with finite fundamental group are globally stable for the pluriclosed flow. This prevents the existence of non-flat homogeneous Bismut Hermitian Einstein (hence also pluriclosed Calabi--Yau with torsion) metrics on C-spaces."},"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":"2307.10207","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2023-07-14T10:09:01Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"5589eed65140374966e7980a4814cb3f43361bd17c477ce0f56af3982d3e6fcd","abstract_canon_sha256":"50f12096660f83215ee1d51472ec59c957bf939612c2e8c83b2fc6a7793594a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:13:33.199330Z","signature_b64":"YUlSG040DWdFweMNgu2dTPmCS/akGapEEUFaCIHDadxYQkV8QQFzFhDs4mFKWo8fBhXMCXG5obiD369J756iBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71f9ba8aee62015a8a13a33a406d7f8a92cf409eefb0cd2582c19539c9ef9bbb","last_reissued_at":"2026-07-05T09:13:33.198824Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:13:33.198824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bismut Hermitian Einstein metrics and the stability of the pluriclosed flow","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Giuseppe Barbaro","submitted_at":"2023-07-14T10:09:01Z","abstract_excerpt":"We compute the (1,1)-Aeppli cohomology of compact simply-connected Lie groups. From this, we deduce that the Bismut flat metrics on the compact Bismut flat manifolds with finite fundamental group are globally stable for the pluriclosed flow. This prevents the existence of non-flat homogeneous Bismut Hermitian Einstein (hence also pluriclosed Calabi--Yau with torsion) metrics on C-spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.10207","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.10207/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":"2307.10207","created_at":"2026-07-05T09:13:33.198881+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.10207v2","created_at":"2026-07-05T09:13:33.198881+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.10207","created_at":"2026-07-05T09:13:33.198881+00:00"},{"alias_kind":"pith_short_12","alias_value":"OH43VCXOMIAV","created_at":"2026-07-05T09:13:33.198881+00:00"},{"alias_kind":"pith_short_16","alias_value":"OH43VCXOMIAVVCQT","created_at":"2026-07-05T09:13:33.198881+00:00"},{"alias_kind":"pith_short_8","alias_value":"OH43VCXO","created_at":"2026-07-05T09:13:33.198881+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.23540","citing_title":"Long-time existence of the pluriclosed flow on some fibrations","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2606.13553","citing_title":"A Levi-type decomposition on two-step solvable Lie algebras with a complex structure","ref_index":104,"is_internal_anchor":false},{"citing_arxiv_id":"2406.07039","citing_title":"Pluriclosed manifolds with parallel Bismut torsion","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2604.22404","citing_title":"On homogeneous HKT manifolds and the Einstein condition","ref_index":3,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OH43VCXOMIAVVCQTUM5EA3L7RK","json":"https://pith.science/pith/OH43VCXOMIAVVCQTUM5EA3L7RK.json","graph_json":"https://pith.science/api/pith-number/OH43VCXOMIAVVCQTUM5EA3L7RK/graph.json","events_json":"https://pith.science/api/pith-number/OH43VCXOMIAVVCQTUM5EA3L7RK/events.json","paper":"https://pith.science/paper/OH43VCXO"},"agent_actions":{"view_html":"https://pith.science/pith/OH43VCXOMIAVVCQTUM5EA3L7RK","download_json":"https://pith.science/pith/OH43VCXOMIAVVCQTUM5EA3L7RK.json","view_paper":"https://pith.science/paper/OH43VCXO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.10207&json=true","fetch_graph":"https://pith.science/api/pith-number/OH43VCXOMIAVVCQTUM5EA3L7RK/graph.json","fetch_events":"https://pith.science/api/pith-number/OH43VCXOMIAVVCQTUM5EA3L7RK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OH43VCXOMIAVVCQTUM5EA3L7RK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OH43VCXOMIAVVCQTUM5EA3L7RK/action/storage_attestation","attest_author":"https://pith.science/pith/OH43VCXOMIAVVCQTUM5EA3L7RK/action/author_attestation","sign_citation":"https://pith.science/pith/OH43VCXOMIAVVCQTUM5EA3L7RK/action/citation_signature","submit_replication":"https://pith.science/pith/OH43VCXOMIAVVCQTUM5EA3L7RK/action/replication_record"}},"created_at":"2026-07-05T09:13:33.198881+00:00","updated_at":"2026-07-05T09:13:33.198881+00:00"}