{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HFNYGWX73HYYDGCRGHVROVHZ5A","short_pith_number":"pith:HFNYGWX7","canonical_record":{"source":{"id":"1406.7381","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-28T10:24:19Z","cross_cats_sorted":[],"title_canon_sha256":"0e66f328eb50fd2e0885d4bace739d0620f58f47dee3de32ab7fe7acb7fd869d","abstract_canon_sha256":"56d693ef9a5a3faa220464374a0c9593b29f3a01a959a678424f81f18cc37c2f"},"schema_version":"1.0"},"canonical_sha256":"395b835affd9f181985131eb1754f9e82d0728959d406cb3eb0f675764a4381e","source":{"kind":"arxiv","id":"1406.7381","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7381","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7381v4","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7381","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"HFNYGWX73HYY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HFNYGWX73HYYDGCR","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HFNYGWX7","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HFNYGWX73HYYDGCRGHVROVHZ5A","target":"record","payload":{"canonical_record":{"source":{"id":"1406.7381","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-28T10:24:19Z","cross_cats_sorted":[],"title_canon_sha256":"0e66f328eb50fd2e0885d4bace739d0620f58f47dee3de32ab7fe7acb7fd869d","abstract_canon_sha256":"56d693ef9a5a3faa220464374a0c9593b29f3a01a959a678424f81f18cc37c2f"},"schema_version":"1.0"},"canonical_sha256":"395b835affd9f181985131eb1754f9e82d0728959d406cb3eb0f675764a4381e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:01.057224Z","signature_b64":"YfApsxnAqT7LfZ7Z5EM9oyZHFLiue5vlb2I/ewgus4pgcDsStnaLX5eRvuH+GZbmu456gKtyshxbe1Is0ymsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"395b835affd9f181985131eb1754f9e82d0728959d406cb3eb0f675764a4381e","last_reissued_at":"2026-05-18T00:01:01.056604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:01.056604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.7381","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nbhEOG/TZNihNXi8Y26RQRVuoE3heGCk95cwqgIjs+EQjW1pM+hhYf/31rEl28y+ritrdrLXel3m6+Scjr8ZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T19:50:30.211876Z"},"content_sha256":"76b300319bad9bc6facf2209adcb6a75708d4783724ce1143bde52a4974c10fe","schema_version":"1.0","event_id":"sha256:76b300319bad9bc6facf2209adcb6a75708d4783724ce1143bde52a4974c10fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HFNYGWX73HYYDGCRGHVROVHZ5A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact regularity of the $\\bar{\\partial}$-problem with dependence on the $\\bar{\\partial}_b$-problem on weakly pseudoconvex domains in $\\mathbb{C}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Dariush Ehsani","submitted_at":"2014-06-28T10:24:19Z","abstract_excerpt":"We reduce the problem of constructing a linear solution operator to the $\\bar{\\partial}$-equation on smoothly bounded weakly pseudoconvex domains, $\\Omega$, in $\\mathbb{C}^2$ to the problem of the boundary $\\bar{\\partial}_b$-equation. We show there is a solution operator to $\\bar{\\partial}$ which is bounded as a map $W^{s}_{(0,1)}(\\Omega)\\cap{ker} \\bar{\\partial} \\rightarrow W^{s}(\\Omega)$ for all $s\\ge 0$ if there is a corresponding solution operator to the $\\bar{\\partial}_b$-problem with analogous regularity properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7381","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wyCkHz4HI3SK5VoNqFFrcJXxOdB8XZ4sRp7RQErWLINkWnyXQR+iVI2q1oDrE/R7fmcihYH80t5dEQ4K21TJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T19:50:30.212217Z"},"content_sha256":"80101a6601d3ee49dea1d6173d394b7b8f95790455a998171a42b23b2060efa8","schema_version":"1.0","event_id":"sha256:80101a6601d3ee49dea1d6173d394b7b8f95790455a998171a42b23b2060efa8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HFNYGWX73HYYDGCRGHVROVHZ5A/bundle.json","state_url":"https://pith.science/pith/HFNYGWX73HYYDGCRGHVROVHZ5A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HFNYGWX73HYYDGCRGHVROVHZ5A/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T19:50:30Z","links":{"resolver":"https://pith.science/pith/HFNYGWX73HYYDGCRGHVROVHZ5A","bundle":"https://pith.science/pith/HFNYGWX73HYYDGCRGHVROVHZ5A/bundle.json","state":"https://pith.science/pith/HFNYGWX73HYYDGCRGHVROVHZ5A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HFNYGWX73HYYDGCRGHVROVHZ5A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HFNYGWX73HYYDGCRGHVROVHZ5A","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":"56d693ef9a5a3faa220464374a0c9593b29f3a01a959a678424f81f18cc37c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-28T10:24:19Z","title_canon_sha256":"0e66f328eb50fd2e0885d4bace739d0620f58f47dee3de32ab7fe7acb7fd869d"},"schema_version":"1.0","source":{"id":"1406.7381","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7381","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7381v4","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7381","created_at":"2026-05-18T00:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"HFNYGWX73HYY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HFNYGWX73HYYDGCR","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HFNYGWX7","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:80101a6601d3ee49dea1d6173d394b7b8f95790455a998171a42b23b2060efa8","target":"graph","created_at":"2026-05-18T00:01:01Z","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 reduce the problem of constructing a linear solution operator to the $\\bar{\\partial}$-equation on smoothly bounded weakly pseudoconvex domains, $\\Omega$, in $\\mathbb{C}^2$ to the problem of the boundary $\\bar{\\partial}_b$-equation. We show there is a solution operator to $\\bar{\\partial}$ which is bounded as a map $W^{s}_{(0,1)}(\\Omega)\\cap{ker} \\bar{\\partial} \\rightarrow W^{s}(\\Omega)$ for all $s\\ge 0$ if there is a corresponding solution operator to the $\\bar{\\partial}_b$-problem with analogous regularity properties.","authors_text":"Dariush Ehsani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-28T10:24:19Z","title":"Exact regularity of the $\\bar{\\partial}$-problem with dependence on the $\\bar{\\partial}_b$-problem on weakly pseudoconvex domains in $\\mathbb{C}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7381","kind":"arxiv","version":4},"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":"sha256:76b300319bad9bc6facf2209adcb6a75708d4783724ce1143bde52a4974c10fe","target":"record","created_at":"2026-05-18T00:01:01Z","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":"56d693ef9a5a3faa220464374a0c9593b29f3a01a959a678424f81f18cc37c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-06-28T10:24:19Z","title_canon_sha256":"0e66f328eb50fd2e0885d4bace739d0620f58f47dee3de32ab7fe7acb7fd869d"},"schema_version":"1.0","source":{"id":"1406.7381","kind":"arxiv","version":4}},"canonical_sha256":"395b835affd9f181985131eb1754f9e82d0728959d406cb3eb0f675764a4381e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"395b835affd9f181985131eb1754f9e82d0728959d406cb3eb0f675764a4381e","first_computed_at":"2026-05-18T00:01:01.056604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:01.056604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YfApsxnAqT7LfZ7Z5EM9oyZHFLiue5vlb2I/ewgus4pgcDsStnaLX5eRvuH+GZbmu456gKtyshxbe1Is0ymsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:01.057224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7381","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76b300319bad9bc6facf2209adcb6a75708d4783724ce1143bde52a4974c10fe","sha256:80101a6601d3ee49dea1d6173d394b7b8f95790455a998171a42b23b2060efa8"],"state_sha256":"63816120a559732072c1c8d0b07bd5492b9900d49a00868c197297b5cfb8f01d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TqkcSdiVbSLC1uhtxB4F0GZJ3dcQ8lMSAhzTaSv974xS/j8A7+5RcCIUFPvphHpgfoBobKrmX/2z09Us+i6IBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T19:50:30.214054Z","bundle_sha256":"29e2da1ced652591f14dd726e9c2b8479abb6db25f50025b2668fe09e38e3b28"}}