{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:O4KD3KPJOOUQOVHL4E2XXW2AYI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d4fbca21afa09191fad52760e7d3316bf854557e583bfaa08a2d122ccebe674c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-09T10:09:53Z","title_canon_sha256":"adb77836dcab122caa97cea9e7b3a71d1239e6cde02d7612c2d284e6731e4a99"},"schema_version":"1.0","source":{"id":"1901.02656","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02656","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02656v1","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02656","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"pith_short_12","alias_value":"O4KD3KPJOOUQ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"O4KD3KPJOOUQOVHL","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"O4KD3KPJ","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:aef2ec6801f10af8200947cc580beff36c21301a8b458d1abbe458d602e80b75","target":"graph","created_at":"2026-05-17T23:56:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove a Bochner type vanishing theorem for compact complex manifolds $Y$ in Fujiki class $\\mathcal C$, with vanishing first Chern class, that admit a cohomology class $[\\alpha] \\in H^{1,1}(Y,\\mathbb R)$ which is numerically effective (nef) and has positive self-intersection (meaning $\\int_Y \\alpha^n \\,>\\, 0$, where $n\\,=\\,\\dim_{\\mathbb C} Y$). Using it, we prove that all holomorphic geometric structures of affine type on such a manifold $Y$ are locally homogeneous on a non-empty Zariski open subset. Consequently, if the geometric structure is rigid in the sense of Gromov, then the fundament","authors_text":"Henri Guenancia, Indranil Biswas, Sorin Dumitrescu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-09T10:09:53Z","title":"A Bochner principle and its applications to Fujiki class $\\mathcal C$ manifolds with vanishing first Chern class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02656","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6d88f78a71d404f554bea9479dcaff49404253755aaec525854796d861266ead","target":"record","created_at":"2026-05-17T23:56:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d4fbca21afa09191fad52760e7d3316bf854557e583bfaa08a2d122ccebe674c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-09T10:09:53Z","title_canon_sha256":"adb77836dcab122caa97cea9e7b3a71d1239e6cde02d7612c2d284e6731e4a99"},"schema_version":"1.0","source":{"id":"1901.02656","kind":"arxiv","version":1}},"canonical_sha256":"77143da9e973a90754ebe1357bdb40c221faa71377cf998bc08ef30f7ee85a38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77143da9e973a90754ebe1357bdb40c221faa71377cf998bc08ef30f7ee85a38","first_computed_at":"2026-05-17T23:56:39.874998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:39.874998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jglTXXxbWv7BW0Dp8EsF3+cQUOVlD8o6ZUQQxVHPjhQfmcPr/zTqlFa2kzRxgAwBd1T4BROXvHHPQzRiHjzNBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:39.875566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.02656","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d88f78a71d404f554bea9479dcaff49404253755aaec525854796d861266ead","sha256:aef2ec6801f10af8200947cc580beff36c21301a8b458d1abbe458d602e80b75"],"state_sha256":"2847eed7202d67b56e0b94b5a5af427c83fce8bb4bdd0eda7280b386d54e6a89"}