{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UICO3C4RPASC5VI655WO4QJFDV","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":"4d8fb4492f207461a3cc29445ece74af3e86859de584d2ac7823d60590bab889","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-15T17:25:08Z","title_canon_sha256":"20cd5a77e08074905531d0dee4f3d6aa13f11502c6b1a3be5a03396025ea5be4"},"schema_version":"1.0","source":{"id":"1506.04677","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04677","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04677v2","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04677","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"UICO3C4RPASC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UICO3C4RPASC5VI6","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UICO3C4R","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:a3eb8f05f4ed7fedfeef768eb2a1e07b86fbd1c561e795f7d787bdffbf1d0334","target":"graph","created_at":"2026-05-18T01:21:23Z","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 revisit uniformly hyperbolic basic sets and the domination of Oseledets splittings at periodic points. We prove that periodic points with simple Lyapunov spectrum are dense in non-trivial basic pieces of Cr-residual diffeomorphisms on three-dimensional manifolds (r >= 1). In the case of the C1-topology we can prove that either all periodic points of a hyperbolic basic piece for a diffeomorphism f have simple spectrum C1- robustly (in which case f has a finest dominated splitting into one-dimensional sub-bundles and all Lyapunov exponent functions of f are continuous in the wea","authors_text":"Jorge Rocha, Mario Bessa, Paulo Varandas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-15T17:25:08Z","title":"Uniform hyperbolicity revisited: Index of periodic points and equidimensional cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04677","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":"sha256:4071ec13889c74ecd35676bad7165fae51f4b9111c31967cf3234d2e4bb97fa5","target":"record","created_at":"2026-05-18T01:21:23Z","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":"4d8fb4492f207461a3cc29445ece74af3e86859de584d2ac7823d60590bab889","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-15T17:25:08Z","title_canon_sha256":"20cd5a77e08074905531d0dee4f3d6aa13f11502c6b1a3be5a03396025ea5be4"},"schema_version":"1.0","source":{"id":"1506.04677","kind":"arxiv","version":2}},"canonical_sha256":"a204ed8b9178242ed51eef6cee41251d516e4ba3fd1dc82277485f762ac20527","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a204ed8b9178242ed51eef6cee41251d516e4ba3fd1dc82277485f762ac20527","first_computed_at":"2026-05-18T01:21:23.034058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:23.034058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7NntNB3TDJSonjRWP9m6rNgwAtJzZr9zPRPOCmr8taSI00cnCTyxIQX0+tS+DG6XCV6K0hb+AArTYFn+D93VBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:23.034723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04677","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4071ec13889c74ecd35676bad7165fae51f4b9111c31967cf3234d2e4bb97fa5","sha256:a3eb8f05f4ed7fedfeef768eb2a1e07b86fbd1c561e795f7d787bdffbf1d0334"],"state_sha256":"c132d0ea712c41b1573a44abfc2ab607e6db2851f5936764caf3fb20bcb7f5ac"}