{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GOYXAJZXRBQHWHBAZVBQOCUI3E","short_pith_number":"pith:GOYXAJZX","schema_version":"1.0","canonical_sha256":"33b170273788607b1c20cd43070a88d91689ca2e30f6cac928c939048c788a1f","source":{"kind":"arxiv","id":"1709.05210","version":1},"attestation_state":"computed","paper":{"title":"Closed almost-K\\\"ahler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are K\\\"ahler","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Markus Upmeier, Mehdi Lejmi","submitted_at":"2017-09-15T13:51:54Z","abstract_excerpt":"We show that a closed almost K\\\"ahler 4-manifold of globally constant holomorphic sectional curvature $k\\geq 0$ with respect to the canonical Hermitian connection is automatically K\\\"ahler. The same result holds for $k<0$ if we require in addition that the Ricci curvature is J-invariant. The proofs are based on the observation that such manifolds are self-dual, so that Chern-Weil theory implies useful integral formulas, which are then combined with results from Seiberg--Witten theory."},"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":"1709.05210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-15T13:51:54Z","cross_cats_sorted":[],"title_canon_sha256":"110bf52339c03f61f3206c7dec39482bc780b8681f90254e3ed0d2e19248993d","abstract_canon_sha256":"b947a5b1224f5ef0a6daffa36ffb98b4c1f77a6a01886fe2324b1096fcc0f4b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:06.402489Z","signature_b64":"iNKokcb1vpEgoUK5yW15oHy0/E04d/Bhy2500ulTisRt4JXZfc0yuOzVRZEYv/bHKR+pygCM+Od/7+9AaGEuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33b170273788607b1c20cd43070a88d91689ca2e30f6cac928c939048c788a1f","last_reissued_at":"2026-05-18T00:35:06.401861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:06.401861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closed almost-K\\\"ahler 4-manifolds of constant non-negative Hermitian holomorphic sectional curvature are K\\\"ahler","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Markus Upmeier, Mehdi Lejmi","submitted_at":"2017-09-15T13:51:54Z","abstract_excerpt":"We show that a closed almost K\\\"ahler 4-manifold of globally constant holomorphic sectional curvature $k\\geq 0$ with respect to the canonical Hermitian connection is automatically K\\\"ahler. The same result holds for $k<0$ if we require in addition that the Ricci curvature is J-invariant. The proofs are based on the observation that such manifolds are self-dual, so that Chern-Weil theory implies useful integral formulas, which are then combined with results from Seiberg--Witten theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05210","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":"1709.05210","created_at":"2026-05-18T00:35:06.401945+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.05210v1","created_at":"2026-05-18T00:35:06.401945+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05210","created_at":"2026-05-18T00:35:06.401945+00:00"},{"alias_kind":"pith_short_12","alias_value":"GOYXAJZXRBQH","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GOYXAJZXRBQHWHBA","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GOYXAJZX","created_at":"2026-05-18T12:31:18.294218+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/GOYXAJZXRBQHWHBAZVBQOCUI3E","json":"https://pith.science/pith/GOYXAJZXRBQHWHBAZVBQOCUI3E.json","graph_json":"https://pith.science/api/pith-number/GOYXAJZXRBQHWHBAZVBQOCUI3E/graph.json","events_json":"https://pith.science/api/pith-number/GOYXAJZXRBQHWHBAZVBQOCUI3E/events.json","paper":"https://pith.science/paper/GOYXAJZX"},"agent_actions":{"view_html":"https://pith.science/pith/GOYXAJZXRBQHWHBAZVBQOCUI3E","download_json":"https://pith.science/pith/GOYXAJZXRBQHWHBAZVBQOCUI3E.json","view_paper":"https://pith.science/paper/GOYXAJZX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.05210&json=true","fetch_graph":"https://pith.science/api/pith-number/GOYXAJZXRBQHWHBAZVBQOCUI3E/graph.json","fetch_events":"https://pith.science/api/pith-number/GOYXAJZXRBQHWHBAZVBQOCUI3E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GOYXAJZXRBQHWHBAZVBQOCUI3E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GOYXAJZXRBQHWHBAZVBQOCUI3E/action/storage_attestation","attest_author":"https://pith.science/pith/GOYXAJZXRBQHWHBAZVBQOCUI3E/action/author_attestation","sign_citation":"https://pith.science/pith/GOYXAJZXRBQHWHBAZVBQOCUI3E/action/citation_signature","submit_replication":"https://pith.science/pith/GOYXAJZXRBQHWHBAZVBQOCUI3E/action/replication_record"}},"created_at":"2026-05-18T00:35:06.401945+00:00","updated_at":"2026-05-18T00:35:06.401945+00:00"}