{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WADEEZILIJJWBQFYYU3IPCESHG","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":"8abf63d147d97030d68b9ea8d5a752fdd455841f9115fdad08f7621bc6740d9d","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-02-05T16:48:02Z","title_canon_sha256":"383839c03650f4b9a7f0fe9254e5e2cc33845f0c82dc087b6943b7f05b432ca5"},"schema_version":"1.0","source":{"id":"2402.06658","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.06658","created_at":"2026-07-05T07:43:36Z"},{"alias_kind":"arxiv_version","alias_value":"2402.06658v1","created_at":"2026-07-05T07:43:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.06658","created_at":"2026-07-05T07:43:36Z"},{"alias_kind":"pith_short_12","alias_value":"WADEEZILIJJW","created_at":"2026-07-05T07:43:36Z"},{"alias_kind":"pith_short_16","alias_value":"WADEEZILIJJWBQFY","created_at":"2026-07-05T07:43:36Z"},{"alias_kind":"pith_short_8","alias_value":"WADEEZIL","created_at":"2026-07-05T07:43:36Z"}],"graph_snapshots":[{"event_id":"sha256:b2ba57af88f6d34c06e7237c3a227a65ff85b3a50c669fb874dd2203dfddd9f8","target":"graph","created_at":"2026-07-05T07:43:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.06658/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate various positivity for singular Hermitian metrics such as Griffiths, $\\omega$-trace and RC, where $\\omega$ is a Hermitian metric, and show that these quasi-positivity notions induce $0$-th cohomology vanishing, rational conected-ness, etc. Here, $\\omega$-trace positivity of smooth Hermitian metrics $h$ on holomorphic vector bundles $E$ represents the positivity of $tr_\\omega i\\Theta_{E,h}$.","authors_text":"Yuta Watanabe","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-02-05T16:48:02Z","title":"$\\omega$-trace and Griffiths positivity for singular Hermitian metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.06658","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":"sha256:25e26043ef9e3a301025f90a8ff0e7c6f63b1bd9a001d3e90934f76495aa500b","target":"record","created_at":"2026-07-05T07:43:36Z","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":"8abf63d147d97030d68b9ea8d5a752fdd455841f9115fdad08f7621bc6740d9d","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-02-05T16:48:02Z","title_canon_sha256":"383839c03650f4b9a7f0fe9254e5e2cc33845f0c82dc087b6943b7f05b432ca5"},"schema_version":"1.0","source":{"id":"2402.06658","kind":"arxiv","version":1}},"canonical_sha256":"b00642650b425360c0b8c5368788923998843e9aa8c4a572bc18d2f602fe4f48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b00642650b425360c0b8c5368788923998843e9aa8c4a572bc18d2f602fe4f48","first_computed_at":"2026-07-05T07:43:36.491001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:43:36.491001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hDTyBFBZqj2vGPVe99de1f2xd0cYMQPJTMi1zYTTNNpgjvWTEivCZquANEBslYNdU5z+D1lG1gM7bjQE9YD/BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:43:36.491364Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.06658","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25e26043ef9e3a301025f90a8ff0e7c6f63b1bd9a001d3e90934f76495aa500b","sha256:b2ba57af88f6d34c06e7237c3a227a65ff85b3a50c669fb874dd2203dfddd9f8"],"state_sha256":"69d997b9af1e0fa26491a9eb8408ad2b8dc1b3740de5add02897d23393ed31c8"}