{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JIMBRESS2OMQWWZVZ2QEZVBZR5","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":"fe438704f5f2b3a9942be35c86ee3916b640058b830bca7be6ca1a9d897e20ec","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-13T10:30:16Z","title_canon_sha256":"5608c2a91eaeb35e25ef6db86999d2284c7e4e065c5f0734c3fcd162ba2176a0"},"schema_version":"1.0","source":{"id":"1106.2410","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2410","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2410v3","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2410","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"pith_short_12","alias_value":"JIMBRESS2OMQ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JIMBRESS2OMQWWZV","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JIMBRESS","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:b76f453d7304384248ee4dac0f2145082ea83a34a81e233dd1e063c723ebb285","target":"graph","created_at":"2026-05-18T03:33:14Z","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 consider a family of $C^1$ vector fields satisfying a suitable higher order involutivity condition. We discuss the definition of commutators, the regularity of Sussmann's orbits and the Poincar\\'e inequality.","authors_text":"Annamaria Montanari, Daniele Morbidelli","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-13T10:30:16Z","title":"Step-s involutive families of vector fields, their orbits and the Poincar\\'e inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2410","kind":"arxiv","version":3},"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":"sha256:59d066d1404b90eb1128e49db4c93a0dd53c229414c2589c5b4a016889e3f34a","target":"record","created_at":"2026-05-18T03:33:14Z","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":"fe438704f5f2b3a9942be35c86ee3916b640058b830bca7be6ca1a9d897e20ec","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-13T10:30:16Z","title_canon_sha256":"5608c2a91eaeb35e25ef6db86999d2284c7e4e065c5f0734c3fcd162ba2176a0"},"schema_version":"1.0","source":{"id":"1106.2410","kind":"arxiv","version":3}},"canonical_sha256":"4a18189252d3990b5b35cea04cd4398f68a00c5d534a280fc9a2e539830ad9d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a18189252d3990b5b35cea04cd4398f68a00c5d534a280fc9a2e539830ad9d7","first_computed_at":"2026-05-18T03:33:14.393169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:14.393169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BtaTpReUKR7R1XI7SYT+7faNXYDnsEEhwBV5BvkczHcE4Q24rrhmpSGQgWY8bi1eYCzaiD82FM6uHbTdu0GfDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:14.393918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2410","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59d066d1404b90eb1128e49db4c93a0dd53c229414c2589c5b4a016889e3f34a","sha256:b76f453d7304384248ee4dac0f2145082ea83a34a81e233dd1e063c723ebb285"],"state_sha256":"da312bf4d77dd65f6b870714194ef900f80e662e1f98ad08f4348facdc909100"}