{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RT2C5QUQSM6XHI4PWAIGFZEG2V","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":"6b6839e7bff2f9574b1cdb9c4f152caf17dd18ac112d93c207dfa831ce032025","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-27T20:59:07Z","title_canon_sha256":"166d8ccda466d7e3b27bf7b765c225795c0721640b756ab1e7a5db9b7333f42a"},"schema_version":"1.0","source":{"id":"1502.08054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.08054","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1502.08054v1","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.08054","created_at":"2026-05-18T02:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"RT2C5QUQSM6X","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RT2C5QUQSM6XHI4P","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RT2C5QUQ","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:651b2ef5fac917c442b0a99a719a32e7abdb60fbab02fb10254c42738bd41f89","target":"graph","created_at":"2026-05-18T02:26:01Z","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 establish $L^2$ extension theorems for $\\bar \\partial$-closed $(0,q)$-forms with values in a holomorphic line bundle with smooth Hermitian metric, from a smooth hypersurface on a Stein manifold. Our result extends (and gives a new, perhaps more classical, proof of) a theorem of Berndtsson on compact K\\\"ahler manifolds, which itself is a sharpening of the theorem of Koziarz. The proof makes use of the Kohn solution, which is the solution of an (interior) elliptic problem, to handle the well-known regularity issues. As such, our methods require the line bundle to be equipped with a smooth met","authors_text":"Dror Varolin, Jeffery D. McNeal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-27T20:59:07Z","title":"$L^2$ Extension of $\\bar\\partial$-closed forms from a hypersurface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.08054","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":"sha256:4292c07aa98e940147241422ea85912aac4d8bd628663ce4cc0c1467e5a08179","target":"record","created_at":"2026-05-18T02:26:01Z","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":"6b6839e7bff2f9574b1cdb9c4f152caf17dd18ac112d93c207dfa831ce032025","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-27T20:59:07Z","title_canon_sha256":"166d8ccda466d7e3b27bf7b765c225795c0721640b756ab1e7a5db9b7333f42a"},"schema_version":"1.0","source":{"id":"1502.08054","kind":"arxiv","version":1}},"canonical_sha256":"8cf42ec290933d73a38fb01062e486d55aacd319205a14b2043783c0a41a8d8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cf42ec290933d73a38fb01062e486d55aacd319205a14b2043783c0a41a8d8b","first_computed_at":"2026-05-18T02:26:01.487276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:01.487276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oVDDUsS2DRuxiJ3GIubp7rGlbxRK2VHNL0nubaI97/2pFb5N3lh1guk4rIr7tkmVgzQsnK0qfSbRXxTxQJGfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:01.487732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.08054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4292c07aa98e940147241422ea85912aac4d8bd628663ce4cc0c1467e5a08179","sha256:651b2ef5fac917c442b0a99a719a32e7abdb60fbab02fb10254c42738bd41f89"],"state_sha256":"249e301e781307c0d1156a82983473fb82c6b64c126030d9050e34a37522e444"}