{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HY5BKDSFXJOZX5KP7NTIRG2LVT","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":"d86f57847f7cec48bed113fabb048e41ca2df47b557528137538cb81dcfb37a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-06-26T21:48:56Z","title_canon_sha256":"8bdbc21c1f4d07571f51df9dfa71c03b350b180008df4a0bbdad8df08d896012"},"schema_version":"1.0","source":{"id":"1306.6367","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.6367","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"1306.6367v2","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6367","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"HY5BKDSFXJOZ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HY5BKDSFXJOZX5KP","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HY5BKDSF","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:938096c325c37c519f134d755547c98995b25211c803b3247f3bc834ede5d654","target":"graph","created_at":"2026-05-18T03:05:08Z","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":"In this note we study several aspects of coisotropic submanifolds of a contact manifold. In particular we give a structure theorem for the singularity of the characteristic foliation of a coisotropic submanifold. Moreover we establish the existence and uniqueness results of germs of contact structures near Legendrian foliations, which is a special case of coisotropic submanifold. This note can be thought of as an attempt to generalize the study of surfaces in three-dimensional contact geometry to higher dimensions.","authors_text":"Yang Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-06-26T21:48:56Z","title":"On Legendrian foliations in contact manifold I: Singularities and neighborhood theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6367","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":"sha256:5bf65dea89e0f93b88d721b51c94c6286ea2ad5b42658e5ab0f4ecee07b15c35","target":"record","created_at":"2026-05-18T03:05:08Z","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":"d86f57847f7cec48bed113fabb048e41ca2df47b557528137538cb81dcfb37a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-06-26T21:48:56Z","title_canon_sha256":"8bdbc21c1f4d07571f51df9dfa71c03b350b180008df4a0bbdad8df08d896012"},"schema_version":"1.0","source":{"id":"1306.6367","kind":"arxiv","version":2}},"canonical_sha256":"3e3a150e45ba5d9bf54ffb66889b4bacf48b1be51041a04370e22f18797c1c82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e3a150e45ba5d9bf54ffb66889b4bacf48b1be51041a04370e22f18797c1c82","first_computed_at":"2026-05-18T03:05:08.513945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:08.513945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M1JRfFMl5QcPT8j4PUp6bptiMcl/eEq6+OVPFydCyA+Y2B+bW5MHGBwWcw154SH4E4s1/LKv7hTMInsJot7GDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:08.514418Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.6367","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bf65dea89e0f93b88d721b51c94c6286ea2ad5b42658e5ab0f4ecee07b15c35","sha256:938096c325c37c519f134d755547c98995b25211c803b3247f3bc834ede5d654"],"state_sha256":"d736c33b8596b098305e3d97ebab23084fbdf919acf2c2ee152632506f42d314"}