{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2P47YLWRG2JXKT3EMPKLYHSU4O","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":"46f3eda445bdda8d5f2b097f41b8c290f3eff3d645c569610439192f99940884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-17T15:22:35Z","title_canon_sha256":"817d819d691c17f7677f82eb0d26d0b4438c6a03c1e5d600973ad9f4d773a896"},"schema_version":"1.0","source":{"id":"1210.4766","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4766","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4766v3","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4766","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"pith_short_12","alias_value":"2P47YLWRG2JX","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2P47YLWRG2JXKT3E","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2P47YLWR","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:5931bdd190e0ea23fc83d93fceafbf796a9f46f3b0e611ac28392895cb0df6ed","target":"graph","created_at":"2026-05-18T03:39:04Z","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":"A partially hyperbolic diffeomorphism $f$ is structurally quasi-stable if for any diffeomorphism $g$ $C^1$-close to $f$, there is a homeomorphism $\\pi$ of $M$ such that $\\pi\\circ g$ and $f\\circ\\pi$ differ only by a motion $\\tau$ along center directions. $f$ is topologically quasi-stable if for any homeomorphism $g$ $C^0$-close to $f$, the above holds for a continuous map $\\pi$ instead of a homeomorphism. We show that any partially hyperbolic diffeomorphism $f$ is topologically quasi-stable, and if $f$ has $C^1$ center foliation $W^c_f$, then $f$ is structurally quasi-stable. As applications we","authors_text":"Huyi Hu, Yujun Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-17T15:22:35Z","title":"Quasi-Stability of Partially Hyperbolic Diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4766","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":"sha256:3424a1804d98b744ebb6ffbed2704f641f6c2b6ae8ea79cfe031aeb1030370c1","target":"record","created_at":"2026-05-18T03:39:04Z","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":"46f3eda445bdda8d5f2b097f41b8c290f3eff3d645c569610439192f99940884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-17T15:22:35Z","title_canon_sha256":"817d819d691c17f7677f82eb0d26d0b4438c6a03c1e5d600973ad9f4d773a896"},"schema_version":"1.0","source":{"id":"1210.4766","kind":"arxiv","version":3}},"canonical_sha256":"d3f9fc2ed13693754f6463d4bc1e54e38454d8b436d1034bcc9022c86d67ecee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3f9fc2ed13693754f6463d4bc1e54e38454d8b436d1034bcc9022c86d67ecee","first_computed_at":"2026-05-18T03:39:04.788277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:04.788277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2UDZsHxGQY4u6mZ3MJF8AUBPFGahzK9m3irQeIC5REiWr/5TpFA2Ie2ukzNsBqKjXLYKPOw7GJfBNNKWKWZMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:04.788725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4766","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3424a1804d98b744ebb6ffbed2704f641f6c2b6ae8ea79cfe031aeb1030370c1","sha256:5931bdd190e0ea23fc83d93fceafbf796a9f46f3b0e611ac28392895cb0df6ed"],"state_sha256":"8f5b83aedeb2728e43df3ca623afd5fd5d20d1e4e0dd9b94848003ca3ece4d00"}