{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:KHET7WGVYKSF3QZJNEQ3ZMREKT","short_pith_number":"pith:KHET7WGV","schema_version":"1.0","canonical_sha256":"51c93fd8d5c2a45dc3296921bcb22454fe659a4707ea7c646660c543a0150b98","source":{"kind":"arxiv","id":"1901.00327","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic pairs in positive-entropy systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bernard Host, Fran\\c{c}ois Blanchard, Sylvie Ruette","submitted_at":"2019-01-02T11:31:45Z","abstract_excerpt":"We show that in a topological dynamical system $(X,T)$ of positive entropy there exist proper (positively) asymptotic pairs, that is, pairs $(x,y)$ such that $x\\not= y$ and $\\lim_{n\\to +\\infty} d(T^n x,T^n y)=0$. More precisely we consider a $T$-ergodic measure $\\mu$ of positive entropy and prove that the set of points that belong to a proper asymptotic pair is of measure $1$. When $T$ is invertible, the stable classes (i.e., the equivalence classes for the asymptotic equivalence) are not stable under $T^{-1}$: for $\\mu$-almost every $x$ there are uncountably many $y$ that are asymptotic with "},"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":"1901.00327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-02T11:31:45Z","cross_cats_sorted":[],"title_canon_sha256":"3288011b8c5bebad45580ed8a573284d0ddeb055b5998cb9e6aaa77678b6cb19","abstract_canon_sha256":"ead2da07d8b03f7efa3b65f117fd2b0cfac75c4210d9760a0483c46aa15cd25e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:06.365604Z","signature_b64":"qJlypUv708BD8Mk3k8BEVJzOF8OALA2YgGrR2arLuoSVdLTXWnsGRKgA+OK2m1IUbiqIdMRKNyxbwvSyBTerBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51c93fd8d5c2a45dc3296921bcb22454fe659a4707ea7c646660c543a0150b98","last_reissued_at":"2026-05-17T23:57:06.365083Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:06.365083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic pairs in positive-entropy systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bernard Host, Fran\\c{c}ois Blanchard, Sylvie Ruette","submitted_at":"2019-01-02T11:31:45Z","abstract_excerpt":"We show that in a topological dynamical system $(X,T)$ of positive entropy there exist proper (positively) asymptotic pairs, that is, pairs $(x,y)$ such that $x\\not= y$ and $\\lim_{n\\to +\\infty} d(T^n x,T^n y)=0$. More precisely we consider a $T$-ergodic measure $\\mu$ of positive entropy and prove that the set of points that belong to a proper asymptotic pair is of measure $1$. When $T$ is invertible, the stable classes (i.e., the equivalence classes for the asymptotic equivalence) are not stable under $T^{-1}$: for $\\mu$-almost every $x$ there are uncountably many $y$ that are asymptotic with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00327","kind":"arxiv","version":1},"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":"1901.00327","created_at":"2026-05-17T23:57:06.365161+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.00327v1","created_at":"2026-05-17T23:57:06.365161+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.00327","created_at":"2026-05-17T23:57:06.365161+00:00"},{"alias_kind":"pith_short_12","alias_value":"KHET7WGVYKSF","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"KHET7WGVYKSF3QZJ","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"KHET7WGV","created_at":"2026-05-18T12:33:21.387695+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/KHET7WGVYKSF3QZJNEQ3ZMREKT","json":"https://pith.science/pith/KHET7WGVYKSF3QZJNEQ3ZMREKT.json","graph_json":"https://pith.science/api/pith-number/KHET7WGVYKSF3QZJNEQ3ZMREKT/graph.json","events_json":"https://pith.science/api/pith-number/KHET7WGVYKSF3QZJNEQ3ZMREKT/events.json","paper":"https://pith.science/paper/KHET7WGV"},"agent_actions":{"view_html":"https://pith.science/pith/KHET7WGVYKSF3QZJNEQ3ZMREKT","download_json":"https://pith.science/pith/KHET7WGVYKSF3QZJNEQ3ZMREKT.json","view_paper":"https://pith.science/paper/KHET7WGV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.00327&json=true","fetch_graph":"https://pith.science/api/pith-number/KHET7WGVYKSF3QZJNEQ3ZMREKT/graph.json","fetch_events":"https://pith.science/api/pith-number/KHET7WGVYKSF3QZJNEQ3ZMREKT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KHET7WGVYKSF3QZJNEQ3ZMREKT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KHET7WGVYKSF3QZJNEQ3ZMREKT/action/storage_attestation","attest_author":"https://pith.science/pith/KHET7WGVYKSF3QZJNEQ3ZMREKT/action/author_attestation","sign_citation":"https://pith.science/pith/KHET7WGVYKSF3QZJNEQ3ZMREKT/action/citation_signature","submit_replication":"https://pith.science/pith/KHET7WGVYKSF3QZJNEQ3ZMREKT/action/replication_record"}},"created_at":"2026-05-17T23:57:06.365161+00:00","updated_at":"2026-05-17T23:57:06.365161+00:00"}