{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:Z4R4HFSAIM764UTX7ARK3QFJTK","short_pith_number":"pith:Z4R4HFSA","schema_version":"1.0","canonical_sha256":"cf23c39640433fee5277f822adc0a99aba76bb62ff18006b0325e99886b0f90b","source":{"kind":"arxiv","id":"1811.12472","version":2},"attestation_state":"computed","paper":{"title":"Empirical measures of partially hyperbolic attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dawei Yang, Jinhua Zhang, Sylvain Crovisier","submitted_at":"2018-11-29T20:31:06Z","abstract_excerpt":"In this paper, we study the limit measures of the empirical measures of Lebesgue almost every point in the basin of a partially hyperbolic attractor. They are strongly related to a notion named Gibbs u-state, which can be defined in a large class of diffeomorphisms with less regularity and which is the same as Pesin-Sinai's notion for partially hyperbolic attractors of $C^{1+\\alpha}$ diffeomorphisms.\n  In particular, we prove that for partially hyperbolic $C^{1+\\alpha}$ diffeomorphisms with one-dimensional center, and for Lebesgue almost every point: (1) the center Lyapunov exponent is well de"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.12472","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-29T20:31:06Z","cross_cats_sorted":[],"title_canon_sha256":"892c9fc16cf024ba3d4438ed3db329432e8fe1a28b9c55e1bb0fc0508b32d28d","abstract_canon_sha256":"0212c2e820a22ffb3c811c1d2a08bea750a0d0dfa69b0e2b5daf6450baf6d43c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:46.385111Z","signature_b64":"L6q1FOAJq7cQfKu+I/n5PGIxouZgw5t2G7/hGJweBL2fbRrHB3zIxoPYmjpOlNvIOjn9Wehwnj23n6FG9+f+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf23c39640433fee5277f822adc0a99aba76bb62ff18006b0325e99886b0f90b","last_reissued_at":"2026-05-17T23:57:46.384577Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:46.384577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Empirical measures of partially hyperbolic attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dawei Yang, Jinhua Zhang, Sylvain Crovisier","submitted_at":"2018-11-29T20:31:06Z","abstract_excerpt":"In this paper, we study the limit measures of the empirical measures of Lebesgue almost every point in the basin of a partially hyperbolic attractor. They are strongly related to a notion named Gibbs u-state, which can be defined in a large class of diffeomorphisms with less regularity and which is the same as Pesin-Sinai's notion for partially hyperbolic attractors of $C^{1+\\alpha}$ diffeomorphisms.\n  In particular, we prove that for partially hyperbolic $C^{1+\\alpha}$ diffeomorphisms with one-dimensional center, and for Lebesgue almost every point: (1) the center Lyapunov exponent is well de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12472","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.12472","created_at":"2026-05-17T23:57:46.384649+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.12472v2","created_at":"2026-05-17T23:57:46.384649+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12472","created_at":"2026-05-17T23:57:46.384649+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z4R4HFSAIM76","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z4R4HFSAIM764UTX","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z4R4HFSA","created_at":"2026-05-18T12:33:04.347982+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z4R4HFSAIM764UTX7ARK3QFJTK","json":"https://pith.science/pith/Z4R4HFSAIM764UTX7ARK3QFJTK.json","graph_json":"https://pith.science/api/pith-number/Z4R4HFSAIM764UTX7ARK3QFJTK/graph.json","events_json":"https://pith.science/api/pith-number/Z4R4HFSAIM764UTX7ARK3QFJTK/events.json","paper":"https://pith.science/paper/Z4R4HFSA"},"agent_actions":{"view_html":"https://pith.science/pith/Z4R4HFSAIM764UTX7ARK3QFJTK","download_json":"https://pith.science/pith/Z4R4HFSAIM764UTX7ARK3QFJTK.json","view_paper":"https://pith.science/paper/Z4R4HFSA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.12472&json=true","fetch_graph":"https://pith.science/api/pith-number/Z4R4HFSAIM764UTX7ARK3QFJTK/graph.json","fetch_events":"https://pith.science/api/pith-number/Z4R4HFSAIM764UTX7ARK3QFJTK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z4R4HFSAIM764UTX7ARK3QFJTK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z4R4HFSAIM764UTX7ARK3QFJTK/action/storage_attestation","attest_author":"https://pith.science/pith/Z4R4HFSAIM764UTX7ARK3QFJTK/action/author_attestation","sign_citation":"https://pith.science/pith/Z4R4HFSAIM764UTX7ARK3QFJTK/action/citation_signature","submit_replication":"https://pith.science/pith/Z4R4HFSAIM764UTX7ARK3QFJTK/action/replication_record"}},"created_at":"2026-05-17T23:57:46.384649+00:00","updated_at":"2026-05-17T23:57:46.384649+00:00"}