{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:DU2MNNAQOIQK4AYDPMBPRR22O5","short_pith_number":"pith:DU2MNNAQ","canonical_record":{"source":{"id":"1007.0775","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-07-05T21:45:20Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"71a9bf1c3dd56c212c3d585017ec5e0b57490ba7d0a3b065a3b5311338badae4","abstract_canon_sha256":"55fb051381e0f2d711d407dc3b77da2594489245001280c008fa8e90f036acbb"},"schema_version":"1.0"},"canonical_sha256":"1d34c6b4107220ae03037b02f8c75a775b7cd1ae04a53eeb10a60fa87f7b8eec","source":{"kind":"arxiv","id":"1007.0775","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0775","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0775v2","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0775","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"pith_short_12","alias_value":"DU2MNNAQOIQK","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DU2MNNAQOIQK4AYD","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DU2MNNAQ","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:DU2MNNAQOIQK4AYDPMBPRR22O5","target":"record","payload":{"canonical_record":{"source":{"id":"1007.0775","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-07-05T21:45:20Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"71a9bf1c3dd56c212c3d585017ec5e0b57490ba7d0a3b065a3b5311338badae4","abstract_canon_sha256":"55fb051381e0f2d711d407dc3b77da2594489245001280c008fa8e90f036acbb"},"schema_version":"1.0"},"canonical_sha256":"1d34c6b4107220ae03037b02f8c75a775b7cd1ae04a53eeb10a60fa87f7b8eec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:24.169978Z","signature_b64":"6hB2Z6f3jJCMMLw3jaAg1ekaG8J/gqWK+8sWtciTodc3mfEKHKuAGRwsiEXex7XP/2Gi9LbpCvnpJbC9bGJRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d34c6b4107220ae03037b02f8c75a775b7cd1ae04a53eeb10a60fa87f7b8eec","last_reissued_at":"2026-05-18T04:42:24.169588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:24.169588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.0775","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:42:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GLkN9AUSh+Goz+54LGyOQzvppVqKsD4XE+Kt+bYaqd5iT6y+B9XSDjGiyP8XYVWZ6Qd+Xw0tL7rLTZUrXD8WBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:39:11.601927Z"},"content_sha256":"e2b3db5ae765b2b41e6431302734f502bad820d0993f2d04de4e7e12b454a617","schema_version":"1.0","event_id":"sha256:e2b3db5ae765b2b41e6431302734f502bad820d0993f2d04de4e7e12b454a617"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:DU2MNNAQOIQK4AYDPMBPRR22O5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The complex Green operator on CR-submanifolds of $\\mathbb{C}^{n}$ of hypersurface type: compactness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Emil J. Straube","submitted_at":"2010-07-05T21:45:20Z","abstract_excerpt":"We establish compactness estimates for $\\overline{\\partial}_{b}$ on a compact pseudoconvex CR-submanifold of $\\mathbb{C}^{n}$ of hypersurface type that satisfies property(P). When the submanifold is orientable, these estimates were proved by A.~Raich via microlocal methods. Our proof deduces the estimates from (a slight extension, when $q>1$, of) those known on hypersurfaces via the fact that locally, CR-submanifolds of hypersurface type are CR-equivalent to a hypersurface. The relationship between two potential theoretic conditions is also clarified."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0775","kind":"arxiv","version":2},"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":"2026-05-18T04:42:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iOrUr6zF4qK49uFB+5IIBKzLEXomOWTV0UiJh4n5LihCMJeIzEG5QhuVISU2vNJ6CbnOn3wj/LOV7o7jaO2OAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:39:11.602281Z"},"content_sha256":"7ef704d070a441e7fe02f2f167f985a1d0f76c502e33d38f22c6a8bc904e55c4","schema_version":"1.0","event_id":"sha256:7ef704d070a441e7fe02f2f167f985a1d0f76c502e33d38f22c6a8bc904e55c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DU2MNNAQOIQK4AYDPMBPRR22O5/bundle.json","state_url":"https://pith.science/pith/DU2MNNAQOIQK4AYDPMBPRR22O5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DU2MNNAQOIQK4AYDPMBPRR22O5/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":"2026-06-03T11:39:11Z","links":{"resolver":"https://pith.science/pith/DU2MNNAQOIQK4AYDPMBPRR22O5","bundle":"https://pith.science/pith/DU2MNNAQOIQK4AYDPMBPRR22O5/bundle.json","state":"https://pith.science/pith/DU2MNNAQOIQK4AYDPMBPRR22O5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DU2MNNAQOIQK4AYDPMBPRR22O5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DU2MNNAQOIQK4AYDPMBPRR22O5","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":"55fb051381e0f2d711d407dc3b77da2594489245001280c008fa8e90f036acbb","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-07-05T21:45:20Z","title_canon_sha256":"71a9bf1c3dd56c212c3d585017ec5e0b57490ba7d0a3b065a3b5311338badae4"},"schema_version":"1.0","source":{"id":"1007.0775","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0775","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0775v2","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0775","created_at":"2026-05-18T04:42:24Z"},{"alias_kind":"pith_short_12","alias_value":"DU2MNNAQOIQK","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DU2MNNAQOIQK4AYD","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DU2MNNAQ","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:7ef704d070a441e7fe02f2f167f985a1d0f76c502e33d38f22c6a8bc904e55c4","target":"graph","created_at":"2026-05-18T04:42:24Z","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 compactness estimates for $\\overline{\\partial}_{b}$ on a compact pseudoconvex CR-submanifold of $\\mathbb{C}^{n}$ of hypersurface type that satisfies property(P). When the submanifold is orientable, these estimates were proved by A.~Raich via microlocal methods. Our proof deduces the estimates from (a slight extension, when $q>1$, of) those known on hypersurfaces via the fact that locally, CR-submanifolds of hypersurface type are CR-equivalent to a hypersurface. The relationship between two potential theoretic conditions is also clarified.","authors_text":"Emil J. Straube","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-07-05T21:45:20Z","title":"The complex Green operator on CR-submanifolds of $\\mathbb{C}^{n}$ of hypersurface type: compactness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0775","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:e2b3db5ae765b2b41e6431302734f502bad820d0993f2d04de4e7e12b454a617","target":"record","created_at":"2026-05-18T04:42:24Z","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":"55fb051381e0f2d711d407dc3b77da2594489245001280c008fa8e90f036acbb","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-07-05T21:45:20Z","title_canon_sha256":"71a9bf1c3dd56c212c3d585017ec5e0b57490ba7d0a3b065a3b5311338badae4"},"schema_version":"1.0","source":{"id":"1007.0775","kind":"arxiv","version":2}},"canonical_sha256":"1d34c6b4107220ae03037b02f8c75a775b7cd1ae04a53eeb10a60fa87f7b8eec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d34c6b4107220ae03037b02f8c75a775b7cd1ae04a53eeb10a60fa87f7b8eec","first_computed_at":"2026-05-18T04:42:24.169588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:24.169588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6hB2Z6f3jJCMMLw3jaAg1ekaG8J/gqWK+8sWtciTodc3mfEKHKuAGRwsiEXex7XP/2Gi9LbpCvnpJbC9bGJRAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:24.169978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0775","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2b3db5ae765b2b41e6431302734f502bad820d0993f2d04de4e7e12b454a617","sha256:7ef704d070a441e7fe02f2f167f985a1d0f76c502e33d38f22c6a8bc904e55c4"],"state_sha256":"4626cb91eb7183d17037339e140f329f5b91def61fd458e206091041c54b9714"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AzhtInZi57cy9pkpXCYK4UJDwX+1uXYMW5iD/PSz8dALRUKRZj6DAbpnIZ1gE+hF3hkmLrgT7Rymk64mO5PpDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T11:39:11.604414Z","bundle_sha256":"262cadd7b57d9e795a993478277ab2067489f50d61779d4716ce3c579edc9649"}}