{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:EHKN3PST3IVZECR2UPKHNUHSNZ","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":"6b48a6a670278ad13ca09893e1d7ce8d4b90a199b23f0f30e9c3307e91bc0ff2","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-02-14T00:37:58Z","title_canon_sha256":"df3b3ca65975fa165ccd37694febd7d80debbd35d84554adb595e94eb9956faf"},"schema_version":"1.0","source":{"id":"0902.2418","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2418","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2418v3","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2418","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"pith_short_12","alias_value":"EHKN3PST3IVZ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"EHKN3PST3IVZECR2","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"EHKN3PST","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:d0fca6f7e250d2e90d2c6aa550def769f3dab261e3f5cf99cc22fe46c0243666","target":"graph","created_at":"2026-05-18T01:23:48Z","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 $(F_t)$ be a smooth flow on a smooth manifold $M$ and $h:M\\to M$ be a smooth orbit preserving map. The following problem is studied: suppose that for every point $z$ of $M$ there exists a germ of a smooth function $f_z$ at $z$ such that near $z$ we have that $h(x)=F_{f_z(x)}(x)$. Can the functions $(f_z)$ be glued together to give a smooth function on all of $M$? This question is closely related to reparametrizations of flows. We describe a large class of flows for which the above problem can be resolved, and show that they have the following property: any smooth flow $(G_t)$ whose orbits ","authors_text":"Sergiy Maksymenko","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-02-14T00:37:58Z","title":"Image of a shift map along the orbits of a flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2418","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:d0045ee591f5f4496c2dd1a983c908a9db51be265e015d42b97da820b1949700","target":"record","created_at":"2026-05-18T01:23:48Z","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":"6b48a6a670278ad13ca09893e1d7ce8d4b90a199b23f0f30e9c3307e91bc0ff2","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-02-14T00:37:58Z","title_canon_sha256":"df3b3ca65975fa165ccd37694febd7d80debbd35d84554adb595e94eb9956faf"},"schema_version":"1.0","source":{"id":"0902.2418","kind":"arxiv","version":3}},"canonical_sha256":"21d4ddbe53da2b920a3aa3d476d0f26e70448bc934346adf2dda41d24a5d7d8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21d4ddbe53da2b920a3aa3d476d0f26e70448bc934346adf2dda41d24a5d7d8f","first_computed_at":"2026-05-18T01:23:48.562833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:48.562833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G03XmItiH+UBViQyX6Wp9QKLXaYM2z1LtI6Kzluqr3U8SGB9+45+jQOh+f88GpWETvKXWW4UKB1uhOqmDrlwAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:48.563459Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.2418","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0045ee591f5f4496c2dd1a983c908a9db51be265e015d42b97da820b1949700","sha256:d0fca6f7e250d2e90d2c6aa550def769f3dab261e3f5cf99cc22fe46c0243666"],"state_sha256":"a36a3d104c91e51f660f4336d7f04daf8b7bbdfdd3db9ffafae1e7917a75e620"}