{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:UEGCROCLP2ZRQTA5LMXL2P5NQF","short_pith_number":"pith:UEGCROCL","schema_version":"1.0","canonical_sha256":"a10c28b84b7eb3184c1d5b2ebd3fad81626765ed5915b47368d56b5c953369e7","source":{"kind":"arxiv","id":"0907.0737","version":2},"attestation_state":"computed","paper":{"title":"Symmetries of degenerate center singularities of plane vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sergiy Maksymenko","submitted_at":"2009-07-04T03:04:48Z","abstract_excerpt":"Let $D$ be a closed unit $2$-disk on the plane centered at the origin $O$, and $F$ be a smooth vector field such that $O$ is a unique singular point of $F$ and all other orbits of $F$ are simple closed curves wrapping once around $O$. Thus topologically $O$ is a \"center\" singularity. Let also $\\mathrm{Diff}(F)$ be the group of all diffeomorphisms of $D$ which preserve orientation and orbits of $F$. In arXiv:0907.0359 the author described the homotopy type of $\\mathrm{Diff}(F)$ under assumption that the $1$-jet of $F$ at $O$ is non-degenerate. In this paper degenerate case is considered. Under "},"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":"0907.0737","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-07-04T03:04:48Z","cross_cats_sorted":[],"title_canon_sha256":"4a8c444210c3277798f0da858d59b71cb5fd86456d49be68a482baf9ee14e485","abstract_canon_sha256":"a63a1463a5be3f723a26195accd12ab4fac340a68d1a67b9985e602a1944ef95"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:48.544668Z","signature_b64":"58RpbUWOPt5u4LhnDnxwpMI8a/KCVA4JP3Tei58r9/qsvFUKTLfRut2/ucokzRYTUDgqqdg3gG+4kdwvHRGwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a10c28b84b7eb3184c1d5b2ebd3fad81626765ed5915b47368d56b5c953369e7","last_reissued_at":"2026-05-18T01:23:48.543935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:48.543935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetries of degenerate center singularities of plane vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sergiy Maksymenko","submitted_at":"2009-07-04T03:04:48Z","abstract_excerpt":"Let $D$ be a closed unit $2$-disk on the plane centered at the origin $O$, and $F$ be a smooth vector field such that $O$ is a unique singular point of $F$ and all other orbits of $F$ are simple closed curves wrapping once around $O$. Thus topologically $O$ is a \"center\" singularity. Let also $\\mathrm{Diff}(F)$ be the group of all diffeomorphisms of $D$ which preserve orientation and orbits of $F$. In arXiv:0907.0359 the author described the homotopy type of $\\mathrm{Diff}(F)$ under assumption that the $1$-jet of $F$ at $O$ is non-degenerate. In this paper degenerate case is considered. Under "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0737","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0907.0737","created_at":"2026-05-18T01:23:48.544053+00:00"},{"alias_kind":"arxiv_version","alias_value":"0907.0737v2","created_at":"2026-05-18T01:23:48.544053+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0737","created_at":"2026-05-18T01:23:48.544053+00:00"},{"alias_kind":"pith_short_12","alias_value":"UEGCROCLP2ZR","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"UEGCROCLP2ZRQTA5","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"UEGCROCL","created_at":"2026-05-18T12:26:02.257875+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/UEGCROCLP2ZRQTA5LMXL2P5NQF","json":"https://pith.science/pith/UEGCROCLP2ZRQTA5LMXL2P5NQF.json","graph_json":"https://pith.science/api/pith-number/UEGCROCLP2ZRQTA5LMXL2P5NQF/graph.json","events_json":"https://pith.science/api/pith-number/UEGCROCLP2ZRQTA5LMXL2P5NQF/events.json","paper":"https://pith.science/paper/UEGCROCL"},"agent_actions":{"view_html":"https://pith.science/pith/UEGCROCLP2ZRQTA5LMXL2P5NQF","download_json":"https://pith.science/pith/UEGCROCLP2ZRQTA5LMXL2P5NQF.json","view_paper":"https://pith.science/paper/UEGCROCL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0907.0737&json=true","fetch_graph":"https://pith.science/api/pith-number/UEGCROCLP2ZRQTA5LMXL2P5NQF/graph.json","fetch_events":"https://pith.science/api/pith-number/UEGCROCLP2ZRQTA5LMXL2P5NQF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UEGCROCLP2ZRQTA5LMXL2P5NQF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UEGCROCLP2ZRQTA5LMXL2P5NQF/action/storage_attestation","attest_author":"https://pith.science/pith/UEGCROCLP2ZRQTA5LMXL2P5NQF/action/author_attestation","sign_citation":"https://pith.science/pith/UEGCROCLP2ZRQTA5LMXL2P5NQF/action/citation_signature","submit_replication":"https://pith.science/pith/UEGCROCLP2ZRQTA5LMXL2P5NQF/action/replication_record"}},"created_at":"2026-05-18T01:23:48.544053+00:00","updated_at":"2026-05-18T01:23:48.544053+00:00"}