{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UXCSZDJQCIXRA5MWDCO2AJWLR5","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":"a599c80c2bc51a850714c31b8f3bd9dba0636dcff06fb80e2ad14f313000a428","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-08T16:44:07Z","title_canon_sha256":"5ac013a7b7076fad78c12b95304698b64b84cb4f643e11857359b8cc18e3de64"},"schema_version":"1.0","source":{"id":"1102.1652","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1652","created_at":"2026-05-18T03:18:18Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1652v2","created_at":"2026-05-18T03:18:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1652","created_at":"2026-05-18T03:18:18Z"},{"alias_kind":"pith_short_12","alias_value":"UXCSZDJQCIXR","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UXCSZDJQCIXRA5MW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UXCSZDJQ","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:0a90dcd25baf23a0df7a4c89bb5ab35e2bd8650b9fd36585c4ff2b9dde15d344","target":"graph","created_at":"2026-05-18T03:18:18Z","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 this paper we deal with an invariant ergodic hyperbolic measure $\\mu$ for a diffeomorphism $f,$ assuming that $f$ it is either $C^{1+\\alpha}$ or $f$ is $C^1$ and the Oseledec splitting of $\\mu$ is dominated. We show that this system $(f,\\mu)$ satisfies a weaker and non-uniform version of specification, related with notions studied in several recent papers, including \\cite{STV,Y, PS, T,Var, Oli}.\n  Our main results have several consequences: as corollaries, we are able to improve the results about quantitative Poincar\\'e recurrence, removing the assumption of the non-uniform specification pr","authors_text":"Krerley Oliveira, Xueting Tian","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-08T16:44:07Z","title":"Non-uniform Hyperbolicity and Non-uniform Specification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1652","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":"sha256:497be9e23001f7c85e6c8bd8cc278822b08cfde8b2e88dbc3e08201ca3196dae","target":"record","created_at":"2026-05-18T03:18:18Z","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":"a599c80c2bc51a850714c31b8f3bd9dba0636dcff06fb80e2ad14f313000a428","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-08T16:44:07Z","title_canon_sha256":"5ac013a7b7076fad78c12b95304698b64b84cb4f643e11857359b8cc18e3de64"},"schema_version":"1.0","source":{"id":"1102.1652","kind":"arxiv","version":2}},"canonical_sha256":"a5c52c8d30122f107596189da026cb8f6a09760220aa0d9b49842fca9e2832a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5c52c8d30122f107596189da026cb8f6a09760220aa0d9b49842fca9e2832a8","first_computed_at":"2026-05-18T03:18:18.850124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:18.850124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XvPWq8afni9NmVHV3LqaVTHuAe5svPV++IPz+PfCKdPuUkRRaUhqjnOR/ne/i24FdTq/R94QIocI+4rBlzLYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:18.850644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1652","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:497be9e23001f7c85e6c8bd8cc278822b08cfde8b2e88dbc3e08201ca3196dae","sha256:0a90dcd25baf23a0df7a4c89bb5ab35e2bd8650b9fd36585c4ff2b9dde15d344"],"state_sha256":"f88ec6742f0f6da077908ce0f840de1cbe0b392bcd1d0831307253574b8afba9"}