{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O4LFQM3IGSZGZLVI35XRCC5QWJ","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":"21a828cf907ab5fba7abb1f0e340bbba8c83fef63532657f9aa14e46f299487e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-11T17:48:06Z","title_canon_sha256":"9ffc1d1da1cff6aac88c3b7a1cd15793aa6729e31a30d23acd8332cc9ebb8f35"},"schema_version":"1.0","source":{"id":"1306.2594","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2594","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2594v2","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2594","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"O4LFQM3IGSZG","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O4LFQM3IGSZGZLVI","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O4LFQM3I","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:5274179a38e8e81553cc38fbbb26fe89019d77b9e181c9d12448041dc2696e76","target":"graph","created_at":"2026-05-18T02:46:22Z","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 the present paper we study the C1-robustness of the three properties: average shadowing, asymptotic average shadowing and limit shadowing within two classes of conservative flows: the incompressible and the Hamiltonian ones. We obtain that the first two properties guarantee dominated splitting (or partial hyperbolicity) on the whole manifold, and the third one implies that the flow is Anosov.","authors_text":"Mario Bessa, Raquel Ribeiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-11T17:48:06Z","title":"Conservative flows with various types of shadowing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2594","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":"sha256:0c5df1efcef76cc3dd1dab6bdc640886371ae2011b150dbf5a40ae5eaea31d26","target":"record","created_at":"2026-05-18T02:46:22Z","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":"21a828cf907ab5fba7abb1f0e340bbba8c83fef63532657f9aa14e46f299487e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-11T17:48:06Z","title_canon_sha256":"9ffc1d1da1cff6aac88c3b7a1cd15793aa6729e31a30d23acd8332cc9ebb8f35"},"schema_version":"1.0","source":{"id":"1306.2594","kind":"arxiv","version":2}},"canonical_sha256":"771658336834b26caea8df6f110bb0b240fe61e5865573c46f2a7e584187241a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"771658336834b26caea8df6f110bb0b240fe61e5865573c46f2a7e584187241a","first_computed_at":"2026-05-18T02:46:22.802994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:22.802994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"roGcrPJJ6Z0B/sLZCoJWdcPkluM+X2hTwpPuGD5zM59cx1wvvkcxPjXxsS2Wkeb0yYW/paanXWA7y/hX44STDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:22.803478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2594","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c5df1efcef76cc3dd1dab6bdc640886371ae2011b150dbf5a40ae5eaea31d26","sha256:5274179a38e8e81553cc38fbbb26fe89019d77b9e181c9d12448041dc2696e76"],"state_sha256":"b334c5b3e243ce1a6952390a0ec9c697a2d31c090b760f66d288a5b715c22111"}