{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZYVYQQMIL7TGNV3XFW3SR6ILDY","short_pith_number":"pith:ZYVYQQMI","schema_version":"1.0","canonical_sha256":"ce2b8841885fe666d7772db728f90b1e142e50eba3da91961c97462662b0adc2","source":{"kind":"arxiv","id":"1504.08191","version":1},"attestation_state":"computed","paper":{"title":"When all closed subsets are recurrent?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jie Li, Piotr Oprocha, Ruifeng Zhang, Xiangdong Ye","submitted_at":"2015-04-30T12:27:23Z","abstract_excerpt":"In the paper we study relations of rigidity, equicontinuity and pointwise recurrence between a t.d.s. $(X,T)$ and the t.d.s. $(K(X),T_K)$ induced on the hyperspace $K(X)$ of all compact subsets of $X$, and provide some characterizations.\n  Among other examples, we construct a minimal, non-equicontinuous, distal and uniformly rigid t.d.s. and a t.d.s. which has dense small periodic sets but does not have dense distal points, solving that way open questions existing in the literature."},"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":"1504.08191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-30T12:27:23Z","cross_cats_sorted":[],"title_canon_sha256":"76fbf01b5d5a367a1580d649124377a2efba34facd4ffa5617f53fea9388ee5c","abstract_canon_sha256":"7dc36f61856ce78733fe45fb16d3330c42839cbeabcd449c7a45be8bcdcd7a35"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:23.072523Z","signature_b64":"aHMkaLXlWCaKLfjKlTJZXACa0wZKKj1nOXvqiToCTUDHGXgspWh8Er7Ojs1c6M5tlSPVBdAeexyvxF4MKHtPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce2b8841885fe666d7772db728f90b1e142e50eba3da91961c97462662b0adc2","last_reissued_at":"2026-05-18T02:17:23.071819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:23.071819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When all closed subsets are recurrent?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jie Li, Piotr Oprocha, Ruifeng Zhang, Xiangdong Ye","submitted_at":"2015-04-30T12:27:23Z","abstract_excerpt":"In the paper we study relations of rigidity, equicontinuity and pointwise recurrence between a t.d.s. $(X,T)$ and the t.d.s. $(K(X),T_K)$ induced on the hyperspace $K(X)$ of all compact subsets of $X$, and provide some characterizations.\n  Among other examples, we construct a minimal, non-equicontinuous, distal and uniformly rigid t.d.s. and a t.d.s. which has dense small periodic sets but does not have dense distal points, solving that way open questions existing in the literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08191","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":"1504.08191","created_at":"2026-05-18T02:17:23.071911+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.08191v1","created_at":"2026-05-18T02:17:23.071911+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08191","created_at":"2026-05-18T02:17:23.071911+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZYVYQQMIL7TG","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZYVYQQMIL7TGNV3X","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZYVYQQMI","created_at":"2026-05-18T12:29:52.810259+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/ZYVYQQMIL7TGNV3XFW3SR6ILDY","json":"https://pith.science/pith/ZYVYQQMIL7TGNV3XFW3SR6ILDY.json","graph_json":"https://pith.science/api/pith-number/ZYVYQQMIL7TGNV3XFW3SR6ILDY/graph.json","events_json":"https://pith.science/api/pith-number/ZYVYQQMIL7TGNV3XFW3SR6ILDY/events.json","paper":"https://pith.science/paper/ZYVYQQMI"},"agent_actions":{"view_html":"https://pith.science/pith/ZYVYQQMIL7TGNV3XFW3SR6ILDY","download_json":"https://pith.science/pith/ZYVYQQMIL7TGNV3XFW3SR6ILDY.json","view_paper":"https://pith.science/paper/ZYVYQQMI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.08191&json=true","fetch_graph":"https://pith.science/api/pith-number/ZYVYQQMIL7TGNV3XFW3SR6ILDY/graph.json","fetch_events":"https://pith.science/api/pith-number/ZYVYQQMIL7TGNV3XFW3SR6ILDY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZYVYQQMIL7TGNV3XFW3SR6ILDY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZYVYQQMIL7TGNV3XFW3SR6ILDY/action/storage_attestation","attest_author":"https://pith.science/pith/ZYVYQQMIL7TGNV3XFW3SR6ILDY/action/author_attestation","sign_citation":"https://pith.science/pith/ZYVYQQMIL7TGNV3XFW3SR6ILDY/action/citation_signature","submit_replication":"https://pith.science/pith/ZYVYQQMIL7TGNV3XFW3SR6ILDY/action/replication_record"}},"created_at":"2026-05-18T02:17:23.071911+00:00","updated_at":"2026-05-18T02:17:23.071911+00:00"}