{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BRZVLMEZKFU37YROHDTG7KWYQE","short_pith_number":"pith:BRZVLMEZ","schema_version":"1.0","canonical_sha256":"0c7355b0995169bfe22e38e66faad88116199dfb7d98631b29188071e90d0b96","source":{"kind":"arxiv","id":"1806.02980","version":3},"attestation_state":"computed","paper":{"title":"Bounded complexity, mean equicontinuity and discrete spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jean-Paul Thouvenot, Jian Li, Leiye Xu, Wen Huang, Xiangdong Ye","submitted_at":"2018-06-08T06:12:22Z","abstract_excerpt":"We study dynamical systems which have bounded complexity with respect to three kinds metrics: the Bowen metric $d_n$, the max-mean metric $\\hat{d}_n$ and the mean metric $\\bar{d}_n$, both in topological dynamics and ergodic theory.\n  It is shown that a topological dynamical system $(X,T)$ has bounded complexity with respect to $d_n$ (resp. $\\hat{d}_n$) if and only if it is equicontinuous (resp. equicontinuous in the mean). However, we construct minimal systems which have bounded complexity with respect to $\\bar{d}_n$ but not equicontinuous in the mean.\n  It turns out that an invariant measure "},"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":"1806.02980","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-06-08T06:12:22Z","cross_cats_sorted":[],"title_canon_sha256":"19687976c656f6936ae94eea7006ba76b6e23f70d0c638ae88e7d14013d80f67","abstract_canon_sha256":"5f1b0b9e8df4183d32fdd74ad6d93db1542a4627b5406fd35d90832d40650db4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:53:44.918137Z","signature_b64":"TZ9fCZl9mcEYpWYcKJaBzUVIoZLhXTFhkUEq0jLxIM6S9B4gmk0UjQgQ0II2p/wEVRZjD4oQfcouH7HdSQh2AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c7355b0995169bfe22e38e66faad88116199dfb7d98631b29188071e90d0b96","last_reissued_at":"2026-07-05T01:53:44.917797Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:53:44.917797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded complexity, mean equicontinuity and discrete spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jean-Paul Thouvenot, Jian Li, Leiye Xu, Wen Huang, Xiangdong Ye","submitted_at":"2018-06-08T06:12:22Z","abstract_excerpt":"We study dynamical systems which have bounded complexity with respect to three kinds metrics: the Bowen metric $d_n$, the max-mean metric $\\hat{d}_n$ and the mean metric $\\bar{d}_n$, both in topological dynamics and ergodic theory.\n  It is shown that a topological dynamical system $(X,T)$ has bounded complexity with respect to $d_n$ (resp. $\\hat{d}_n$) if and only if it is equicontinuous (resp. equicontinuous in the mean). However, we construct minimal systems which have bounded complexity with respect to $\\bar{d}_n$ but not equicontinuous in the mean.\n  It turns out that an invariant measure "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02980","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1806.02980/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1806.02980","created_at":"2026-07-05T01:53:44.917852+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.02980v3","created_at":"2026-07-05T01:53:44.917852+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02980","created_at":"2026-07-05T01:53:44.917852+00:00"},{"alias_kind":"pith_short_12","alias_value":"BRZVLMEZKFU3","created_at":"2026-07-05T01:53:44.917852+00:00"},{"alias_kind":"pith_short_16","alias_value":"BRZVLMEZKFU37YRO","created_at":"2026-07-05T01:53:44.917852+00:00"},{"alias_kind":"pith_short_8","alias_value":"BRZVLMEZ","created_at":"2026-07-05T01:53:44.917852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.08434","citing_title":"Discrete spectrum for amenable group actions","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BRZVLMEZKFU37YROHDTG7KWYQE","json":"https://pith.science/pith/BRZVLMEZKFU37YROHDTG7KWYQE.json","graph_json":"https://pith.science/api/pith-number/BRZVLMEZKFU37YROHDTG7KWYQE/graph.json","events_json":"https://pith.science/api/pith-number/BRZVLMEZKFU37YROHDTG7KWYQE/events.json","paper":"https://pith.science/paper/BRZVLMEZ"},"agent_actions":{"view_html":"https://pith.science/pith/BRZVLMEZKFU37YROHDTG7KWYQE","download_json":"https://pith.science/pith/BRZVLMEZKFU37YROHDTG7KWYQE.json","view_paper":"https://pith.science/paper/BRZVLMEZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.02980&json=true","fetch_graph":"https://pith.science/api/pith-number/BRZVLMEZKFU37YROHDTG7KWYQE/graph.json","fetch_events":"https://pith.science/api/pith-number/BRZVLMEZKFU37YROHDTG7KWYQE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BRZVLMEZKFU37YROHDTG7KWYQE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BRZVLMEZKFU37YROHDTG7KWYQE/action/storage_attestation","attest_author":"https://pith.science/pith/BRZVLMEZKFU37YROHDTG7KWYQE/action/author_attestation","sign_citation":"https://pith.science/pith/BRZVLMEZKFU37YROHDTG7KWYQE/action/citation_signature","submit_replication":"https://pith.science/pith/BRZVLMEZKFU37YROHDTG7KWYQE/action/replication_record"}},"created_at":"2026-07-05T01:53:44.917852+00:00","updated_at":"2026-07-05T01:53:44.917852+00:00"}