{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:S6YA4T2AL7M7DXN4TJZW5LR5E6","short_pith_number":"pith:S6YA4T2A","schema_version":"1.0","canonical_sha256":"97b00e4f405fd9f1ddbc9a736eae3d27ac0f3427b55484fec105592e6863735c","source":{"kind":"arxiv","id":"1810.05085","version":2},"attestation_state":"computed","paper":{"title":"On the centralizer of vector fields: criteria of triviality and genericity results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Bruno Santiago, Davi Obata, Martin Leguil","submitted_at":"2018-10-11T15:32:55Z","abstract_excerpt":"In this paper, we investigate the question of whether a typical vector field on a compact connected Riemannian manifold $M^d$ has a `small' centralizer. In the $C^1$ case, we give two criteria, one of which is $C^1$-generic, which guarantees that the centralizer of a $C^1$-generic vector field is indeed small, namely \\textit{collinear}. The other criterion states that a $C^1$ \\textit{separating} flow has a collinear $C^1$-centralizer. When all the singularities are hyperbolic, we prove that the collinearity property can actually be promoted to a stronger one, refered as \\textit{quasi-trivialit"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.05085","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-10-11T15:32:55Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"660849eeba425b267ab2f5153a070f83cea88fe4bf0333e82d69c0cc1c7f992a","abstract_canon_sha256":"4b48ddf4cd5ae43aa85106c8a39a94f72296fbee244dce7ac757b2b7fb71cbc1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:44:38.362266Z","signature_b64":"wH5pXbyrQ7fM2D6X15HquaGac5czuM2p2UV+cbRAwGGuZghzGR3HbSeFCCOB0hCKyWEKh6KxBU5zhZ8758KqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97b00e4f405fd9f1ddbc9a736eae3d27ac0f3427b55484fec105592e6863735c","last_reissued_at":"2026-07-05T04:44:38.361811Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:44:38.361811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the centralizer of vector fields: criteria of triviality and genericity results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Bruno Santiago, Davi Obata, Martin Leguil","submitted_at":"2018-10-11T15:32:55Z","abstract_excerpt":"In this paper, we investigate the question of whether a typical vector field on a compact connected Riemannian manifold $M^d$ has a `small' centralizer. In the $C^1$ case, we give two criteria, one of which is $C^1$-generic, which guarantees that the centralizer of a $C^1$-generic vector field is indeed small, namely \\textit{collinear}. The other criterion states that a $C^1$ \\textit{separating} flow has a collinear $C^1$-centralizer. When all the singularities are hyperbolic, we prove that the collinearity property can actually be promoted to a stronger one, refered as \\textit{quasi-trivialit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05085","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.05085/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.05085","created_at":"2026-07-05T04:44:38.361866+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.05085v2","created_at":"2026-07-05T04:44:38.361866+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05085","created_at":"2026-07-05T04:44:38.361866+00:00"},{"alias_kind":"pith_short_12","alias_value":"S6YA4T2AL7M7","created_at":"2026-07-05T04:44:38.361866+00:00"},{"alias_kind":"pith_short_16","alias_value":"S6YA4T2AL7M7DXN4","created_at":"2026-07-05T04:44:38.361866+00:00"},{"alias_kind":"pith_short_8","alias_value":"S6YA4T2A","created_at":"2026-07-05T04:44:38.361866+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S6YA4T2AL7M7DXN4TJZW5LR5E6","json":"https://pith.science/pith/S6YA4T2AL7M7DXN4TJZW5LR5E6.json","graph_json":"https://pith.science/api/pith-number/S6YA4T2AL7M7DXN4TJZW5LR5E6/graph.json","events_json":"https://pith.science/api/pith-number/S6YA4T2AL7M7DXN4TJZW5LR5E6/events.json","paper":"https://pith.science/paper/S6YA4T2A"},"agent_actions":{"view_html":"https://pith.science/pith/S6YA4T2AL7M7DXN4TJZW5LR5E6","download_json":"https://pith.science/pith/S6YA4T2AL7M7DXN4TJZW5LR5E6.json","view_paper":"https://pith.science/paper/S6YA4T2A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.05085&json=true","fetch_graph":"https://pith.science/api/pith-number/S6YA4T2AL7M7DXN4TJZW5LR5E6/graph.json","fetch_events":"https://pith.science/api/pith-number/S6YA4T2AL7M7DXN4TJZW5LR5E6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S6YA4T2AL7M7DXN4TJZW5LR5E6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S6YA4T2AL7M7DXN4TJZW5LR5E6/action/storage_attestation","attest_author":"https://pith.science/pith/S6YA4T2AL7M7DXN4TJZW5LR5E6/action/author_attestation","sign_citation":"https://pith.science/pith/S6YA4T2AL7M7DXN4TJZW5LR5E6/action/citation_signature","submit_replication":"https://pith.science/pith/S6YA4T2AL7M7DXN4TJZW5LR5E6/action/replication_record"}},"created_at":"2026-07-05T04:44:38.361866+00:00","updated_at":"2026-07-05T04:44:38.361866+00:00"}