{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PYCLOYWQI4GAQOEIE6LNUQFAWS","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":"e64123c09f49f9604d2108166f1d158c994b98b9abc773fdf4684a6df9f632a8","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-07-25T08:11:36Z","title_canon_sha256":"4ad770e14528442f8e7b5ddfcd12c1b839dfb2c7f27e332da4bb2994cfc4f97f"},"schema_version":"1.0","source":{"id":"2607.23094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23094","created_at":"2026-07-28T01:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23094v1","created_at":"2026-07-28T01:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23094","created_at":"2026-07-28T01:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"PYCLOYWQI4GA","created_at":"2026-07-28T01:22:06Z"},{"alias_kind":"pith_short_16","alias_value":"PYCLOYWQI4GAQOEI","created_at":"2026-07-28T01:22:06Z"},{"alias_kind":"pith_short_8","alias_value":"PYCLOYWQ","created_at":"2026-07-28T01:22:06Z"}],"graph_snapshots":[{"event_id":"sha256:35b7e481990ce08160c55f3bf02325648184b905b9aa1a37f8006c77feaa24a2","target":"graph","created_at":"2026-07-28T01:22:06Z","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/2607.23094/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce Siu's curvature operator \\(A^E_{p,q}\\) for vector-bundle-valued differential forms on K\\\"ahler manifolds. When $p=n$, this operator reduces to the classical Akizuki--Nakano curvature operator. We first characterize the semipositivity of \\(A^E_{p,q}\\) in terms of an optimal \\(L^2\\)-estimate condition for the \\(\\bar\\partial\\)-operator, and then prove an Ohsawa--Takegoshi-type extension theorem for \\(E\\)-valued \\((p,q)\\)-forms under the curvature condition \\(A^E_{p,q+1}\\geq0\\), using a new twisted basic estimate adapted to this setting. As an application, we prove the ","authors_text":"Gang Huang","cross_cats":["math.AG","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-07-25T08:11:36Z","title":"Siu's curvature positivity and $L^2$ extension theorems for $(p,q)$-forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23094","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:d3d0160e23e4b1adf2e0acf5ecc68326814c09171e455605aec6a4ae8a453393","target":"record","created_at":"2026-07-28T01:22:06Z","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":"e64123c09f49f9604d2108166f1d158c994b98b9abc773fdf4684a6df9f632a8","cross_cats_sorted":["math.AG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-07-25T08:11:36Z","title_canon_sha256":"4ad770e14528442f8e7b5ddfcd12c1b839dfb2c7f27e332da4bb2994cfc4f97f"},"schema_version":"1.0","source":{"id":"2607.23094","kind":"arxiv","version":1}},"canonical_sha256":"7e04b762d0470c0838882796da40a0b4ba0c845332eef27003cd12604570b7b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e04b762d0470c0838882796da40a0b4ba0c845332eef27003cd12604570b7b9","first_computed_at":"2026-07-28T01:22:06.454838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:22:06.454838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YNcT8JbwV9C7n+VU4W0yfqQLZuTdn56N7fkCQalID0WFle5LROH9cbG3pVvL5XoI+LvlUYe8QwklvshZwf67Bg==","signature_status":"signed_v1","signed_at":"2026-07-28T01:22:06.456527Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3d0160e23e4b1adf2e0acf5ecc68326814c09171e455605aec6a4ae8a453393","sha256:35b7e481990ce08160c55f3bf02325648184b905b9aa1a37f8006c77feaa24a2"],"state_sha256":"d546283f10552a909a720adc505f5a37aebceb13ada1e5f8e786b49f0992e5b3"}