{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:WADEEZILIJJWBQFYYU3IPCESHG","short_pith_number":"pith:WADEEZIL","schema_version":"1.0","canonical_sha256":"b00642650b425360c0b8c5368788923998843e9aa8c4a572bc18d2f602fe4f48","source":{"kind":"arxiv","id":"2402.06658","version":1},"attestation_state":"computed","paper":{"title":"$\\omega$-trace and Griffiths positivity for singular Hermitian metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Yuta Watanabe","submitted_at":"2024-02-05T16:48:02Z","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 $tr_\\omega i\\Theta_{E,h}$."},"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":"2402.06658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-02-05T16:48:02Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"383839c03650f4b9a7f0fe9254e5e2cc33845f0c82dc087b6943b7f05b432ca5","abstract_canon_sha256":"8abf63d147d97030d68b9ea8d5a752fdd455841f9115fdad08f7621bc6740d9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:43:36.491364Z","signature_b64":"hDTyBFBZqj2vGPVe99de1f2xd0cYMQPJTMi1zYTTNNpgjvWTEivCZquANEBslYNdU5z+D1lG1gM7bjQE9YD/BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b00642650b425360c0b8c5368788923998843e9aa8c4a572bc18d2f602fe4f48","last_reissued_at":"2026-07-05T07:43:36.491001Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:43:36.491001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\omega$-trace and Griffiths positivity for singular Hermitian metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Yuta Watanabe","submitted_at":"2024-02-05T16:48:02Z","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 $tr_\\omega i\\Theta_{E,h}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.06658","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.06658/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":"2402.06658","created_at":"2026-07-05T07:43:36.491067+00:00"},{"alias_kind":"arxiv_version","alias_value":"2402.06658v1","created_at":"2026-07-05T07:43:36.491067+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.06658","created_at":"2026-07-05T07:43:36.491067+00:00"},{"alias_kind":"pith_short_12","alias_value":"WADEEZILIJJW","created_at":"2026-07-05T07:43:36.491067+00:00"},{"alias_kind":"pith_short_16","alias_value":"WADEEZILIJJWBQFY","created_at":"2026-07-05T07:43:36.491067+00:00"},{"alias_kind":"pith_short_8","alias_value":"WADEEZIL","created_at":"2026-07-05T07:43:36.491067+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/WADEEZILIJJWBQFYYU3IPCESHG","json":"https://pith.science/pith/WADEEZILIJJWBQFYYU3IPCESHG.json","graph_json":"https://pith.science/api/pith-number/WADEEZILIJJWBQFYYU3IPCESHG/graph.json","events_json":"https://pith.science/api/pith-number/WADEEZILIJJWBQFYYU3IPCESHG/events.json","paper":"https://pith.science/paper/WADEEZIL"},"agent_actions":{"view_html":"https://pith.science/pith/WADEEZILIJJWBQFYYU3IPCESHG","download_json":"https://pith.science/pith/WADEEZILIJJWBQFYYU3IPCESHG.json","view_paper":"https://pith.science/paper/WADEEZIL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2402.06658&json=true","fetch_graph":"https://pith.science/api/pith-number/WADEEZILIJJWBQFYYU3IPCESHG/graph.json","fetch_events":"https://pith.science/api/pith-number/WADEEZILIJJWBQFYYU3IPCESHG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WADEEZILIJJWBQFYYU3IPCESHG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WADEEZILIJJWBQFYYU3IPCESHG/action/storage_attestation","attest_author":"https://pith.science/pith/WADEEZILIJJWBQFYYU3IPCESHG/action/author_attestation","sign_citation":"https://pith.science/pith/WADEEZILIJJWBQFYYU3IPCESHG/action/citation_signature","submit_replication":"https://pith.science/pith/WADEEZILIJJWBQFYYU3IPCESHG/action/replication_record"}},"created_at":"2026-07-05T07:43:36.491067+00:00","updated_at":"2026-07-05T07:43:36.491067+00:00"}