{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YVCI24JWCC7VXXRD7EUYLX64JT","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":"f5cd99dbc7814ad5433434c0a83a3ad555e92a3faa52ac9e0790b9fafa66d4c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-10T06:53:32Z","title_canon_sha256":"84ad79b06097971feab6d83bc4969dc9b54ff34fe9b1e2e57e103d62881609bb"},"schema_version":"1.0","source":{"id":"1805.03848","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03848","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03848v2","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03848","created_at":"2026-05-18T00:16:13Z"},{"alias_kind":"pith_short_12","alias_value":"YVCI24JWCC7V","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YVCI24JWCC7VXXRD","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YVCI24JW","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:6ea67a8d34501e64ecc904e33399859f2f4ca2293b2f9ffb471fb80dbf08beb7","target":"graph","created_at":"2026-05-18T00:16:13Z","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":"We show that certain types of the three-legged accessibility property of a partially hyperbolic diffeomorphism imply the existence of a unique minimal set for one strong foliation and the transitivity of the other one. In case the center dimension is one, we also give a criteria to obtain three-legged accessibility in a robust way. We show some applications of our results to the time-one map of Anosov flows, skew products and certain Anosov diffeomorphisms with partially hyperbolic splitting.","authors_text":"Jana Rodriguez Hertz, Ra\\'ul Ures","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-10T06:53:32Z","title":"On the three-legged accessibility property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03848","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:b9595a730fbd68f30e30d1ef3ade36393bc903e2e46dca7365b2e93883387c4e","target":"record","created_at":"2026-05-18T00:16:13Z","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":"f5cd99dbc7814ad5433434c0a83a3ad555e92a3faa52ac9e0790b9fafa66d4c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-10T06:53:32Z","title_canon_sha256":"84ad79b06097971feab6d83bc4969dc9b54ff34fe9b1e2e57e103d62881609bb"},"schema_version":"1.0","source":{"id":"1805.03848","kind":"arxiv","version":2}},"canonical_sha256":"c5448d713610bf5bde23f92985dfdc4ccc998c08ca5601e92361ab356a68d2f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5448d713610bf5bde23f92985dfdc4ccc998c08ca5601e92361ab356a68d2f0","first_computed_at":"2026-05-18T00:16:13.623936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:13.623936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2xig6lXi9VQE+MukZJDRfqzHkvhUac6UTEYOx9Y8nLMyl3LJoJJygiC5t5+ITgcheo3zdqV3+oEEltuRqCGDBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:13.624628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.03848","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9595a730fbd68f30e30d1ef3ade36393bc903e2e46dca7365b2e93883387c4e","sha256:6ea67a8d34501e64ecc904e33399859f2f4ca2293b2f9ffb471fb80dbf08beb7"],"state_sha256":"cde58f8f7963947ba50e2505c4fdd770bee9671df1fc6b7e8ba689d92090c387"}