{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UWJ7ZTRESR3N27BO5YKUKJYJVF","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":"b37fc90335ea40452fa50ceec85e489d5eed1026be85a52cbf62da6c443cc860","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-08T23:20:37Z","title_canon_sha256":"0cd40faa1a31ea8cf2ad240bdcef7bab55db8bba6616271a9ab8bff8089069b0"},"schema_version":"1.0","source":{"id":"1811.03715","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03715","created_at":"2026-05-17T23:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03715v2","created_at":"2026-05-17T23:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03715","created_at":"2026-05-17T23:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"UWJ7ZTRESR3N","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UWJ7ZTRESR3N27BO","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UWJ7ZTRE","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:8935d7f426a1cacc554d23474700868c03d1c4ec5a909f0adeed8e28e13bd834","target":"graph","created_at":"2026-05-17T23:58:13Z","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 modified form of the classical Morrey-Kohn-H\\\"ormander identity, adapted to pseudoconcave boundaries. Applying this result to an annulus between two bounded pseudoconvex domains in $\\mathbb{C}^n$, where the inner domain has\n  $\\mathcal{C}^{1,1}$ boundary, we show that the $L^2$ Dolbeault cohomology group in bidegree $(p,q)$ vanishes if $1\\leq q\\leq n-2$ and is Hausdorff and infinite-dimensional if $q=n-1$, so that the Cauchy-Riemann operator has closed range in each bidegree. As a dual result, we prove that the Cauchy-Riemann operator is solvable in the $L^2$ Sobolev space $W^1$ on ","authors_text":"Debraj Chakrabarti, Phillip S. Harrington","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-08T23:20:37Z","title":"A Modified Morrey-Kohn-H\\\"ormander Identity and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03715","kind":"arxiv","version":2},"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":"sha256:00a408a8c15a63406b7f5ca2073ade553666e33c970793bce9c74bc9b79fa077","target":"record","created_at":"2026-05-17T23:58:13Z","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":"b37fc90335ea40452fa50ceec85e489d5eed1026be85a52cbf62da6c443cc860","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-08T23:20:37Z","title_canon_sha256":"0cd40faa1a31ea8cf2ad240bdcef7bab55db8bba6616271a9ab8bff8089069b0"},"schema_version":"1.0","source":{"id":"1811.03715","kind":"arxiv","version":2}},"canonical_sha256":"a593fcce249476dd7c2eee15452709a96059f2153475a3ca0ef0b15bdc6510e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a593fcce249476dd7c2eee15452709a96059f2153475a3ca0ef0b15bdc6510e3","first_computed_at":"2026-05-17T23:58:13.471257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:13.471257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7s0ZOSp+PrKbZUc68IZXiMYKz3TnpuHmR8nON7EdW/pj9SlcY/ugc8KUY627d1XQWBD4KbE+WsWKjXAcme8qDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:13.471705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.03715","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00a408a8c15a63406b7f5ca2073ade553666e33c970793bce9c74bc9b79fa077","sha256:8935d7f426a1cacc554d23474700868c03d1c4ec5a909f0adeed8e28e13bd834"],"state_sha256":"63bcbbaef58d422f13ef4310e82e636f2c8b505cb2df592309f8237180c0886e"}