{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UHAMYJB3QAIICYU6KG4223LOOW","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":"fba30f1bdf101255378b23016a6aeb4e42ebe617b2ac5bd65564888e2fe3ea7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-10T16:58:04Z","title_canon_sha256":"db3e6d164486dd81d4f024c58c96fb1820ee947273b660fd40e8bd5c3cb02adf"},"schema_version":"1.0","source":{"id":"1904.05295","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.05295","created_at":"2026-07-05T01:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1904.05295v1","created_at":"2026-07-05T01:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05295","created_at":"2026-07-05T01:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"UHAMYJB3QAII","created_at":"2026-07-05T01:27:17Z"},{"alias_kind":"pith_short_16","alias_value":"UHAMYJB3QAIICYU6","created_at":"2026-07-05T01:27:17Z"},{"alias_kind":"pith_short_8","alias_value":"UHAMYJB3","created_at":"2026-07-05T01:27:17Z"}],"graph_snapshots":[{"event_id":"sha256:48a9fd6ade6ff93cd30dc83f97341624bf8ceb2f71542f104af8f147a6d315cc","target":"graph","created_at":"2026-07-05T01:27:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1904.05295/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study transitive partially hyperbolic diffeomorphisms with one-dimensional topologically neutral center, meaning that the length of the iterate of small center segments remains small. Such systems are dynamically coherent. We show that there exists a continuous metric along the center foliation which is invariant under the dynamics. As an application, we classify the transitive partially hyperbolic diffeomorphisms on 3-manifolds with topologically neutral center.","authors_text":"Christian Bonatti, Jinhua Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-10T16:58:04Z","title":"Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05295","kind":"arxiv","version":1},"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:e36326f22c6de71934ba988179ab730344685af35e9a509d54c2d52ba70b5983","target":"record","created_at":"2026-07-05T01:27:17Z","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":"fba30f1bdf101255378b23016a6aeb4e42ebe617b2ac5bd65564888e2fe3ea7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-10T16:58:04Z","title_canon_sha256":"db3e6d164486dd81d4f024c58c96fb1820ee947273b660fd40e8bd5c3cb02adf"},"schema_version":"1.0","source":{"id":"1904.05295","kind":"arxiv","version":1}},"canonical_sha256":"a1c0cc243b801081629e51b9ad6d6e75993ec524f8845a103bc41bdcb13dfabe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1c0cc243b801081629e51b9ad6d6e75993ec524f8845a103bc41bdcb13dfabe","first_computed_at":"2026-07-05T01:27:17.638079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:27:17.638079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OYBJhBi4xMlvltOsrhWIgcx0onCWGdL06jzzLMYNZECnXsLbRd8AIUjUueg1jGHLhiAMa5WZUidwR7/7k4aXBw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:27:17.638494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.05295","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e36326f22c6de71934ba988179ab730344685af35e9a509d54c2d52ba70b5983","sha256:48a9fd6ade6ff93cd30dc83f97341624bf8ceb2f71542f104af8f147a6d315cc"],"state_sha256":"c1d4ec93905da7b348b1e7c57c5b76b4da245c751061103a9768fc81a2bd1fd7"}