{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VDGSVIU7AM4D2LT3FV4FCE5GRW","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":"2a9b96ac5d52d71137652d11c65f4011f41cb8a0e6137aac3588060846b9fd04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-07T03:10:17Z","title_canon_sha256":"cb3549f87dc93600b5ce3b32789f1131bd75829bd356b0a33b143841aba58027"},"schema_version":"1.0","source":{"id":"1802.02294","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.02294","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"arxiv_version","alias_value":"1802.02294v1","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.02294","created_at":"2026-05-18T00:24:08Z"},{"alias_kind":"pith_short_12","alias_value":"VDGSVIU7AM4D","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VDGSVIU7AM4D2LT3","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VDGSVIU7","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:03ebc8a1834524bfdaadef31c644c0c6ee5c54142d2e3ff05aafa2b8c1de34a2","target":"graph","created_at":"2026-05-18T00:24:08Z","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":"Let $M^{2n+1}$, $n\\ge 1$, be a smooth manifold with a pseudo-convex integrable CR structure of hypersurface type. We consider a sequence of CR invariant subsets $ M=\\mathcal S_0 \\supset \\mathcal S_1 \\supset \\cdots \\supset \\mathcal S_{n}, $ where $\\mathcal S_q$ is the set of points where the Levi-form has nullity $\\ge q$. We prove that $\\mathcal S_q$'s are locally given as common zero sets of the coefficients $A_j,$ $j=0,1,\\ldots, q-1,$ of the characteristic polynomial of the Levi-form. Some sufficient conditions for local existence of complex submanifolds are presented in terms of the coeffici","authors_text":"Chong-Kyu Han, Kuerak Chung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-07T03:10:17Z","title":"Nullity of the Levi-form and the associated subvarieties for pseudo-convex CR structures of hypersurface type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02294","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":"sha256:60372a25602f698bddb616de1f426e85bb50c71edbbaa8af0118d406cf8213ef","target":"record","created_at":"2026-05-18T00:24:08Z","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":"2a9b96ac5d52d71137652d11c65f4011f41cb8a0e6137aac3588060846b9fd04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-07T03:10:17Z","title_canon_sha256":"cb3549f87dc93600b5ce3b32789f1131bd75829bd356b0a33b143841aba58027"},"schema_version":"1.0","source":{"id":"1802.02294","kind":"arxiv","version":1}},"canonical_sha256":"a8cd2aa29f03383d2e7b2d785113a68db7ec7cad2a480b81b1164a28a64970c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8cd2aa29f03383d2e7b2d785113a68db7ec7cad2a480b81b1164a28a64970c7","first_computed_at":"2026-05-18T00:24:08.639255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:08.639255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JGAhai6nr7Thg23UBYwVkAHoSkgEbNAepJE3cRGkcVwI/dbESBn6sM+dKFIznywB7csGVplpA+ud3g2isNOJBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:08.639837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.02294","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60372a25602f698bddb616de1f426e85bb50c71edbbaa8af0118d406cf8213ef","sha256:03ebc8a1834524bfdaadef31c644c0c6ee5c54142d2e3ff05aafa2b8c1de34a2"],"state_sha256":"a3a27df6df458381ff978fdfe5b8940fad66eb97b91a2673fb71d227f22a2f29"}