{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GY5U3UXL3774ON6C7ZCYP6ZMTC","short_pith_number":"pith:GY5U3UXL","schema_version":"1.0","canonical_sha256":"363b4dd2ebdfffc737c2fe4587fb2c989f7676e72ec5b3060a18bdc3d7216065","source":{"kind":"arxiv","id":"1801.04445","version":1},"attestation_state":"computed","paper":{"title":"On distributional chaos in non-autonomous discrete systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hao Zhu, Hua Shao, Yuming Shi","submitted_at":"2018-01-13T14:20:24Z","abstract_excerpt":"This paper studies distributional chaos in non-autonomous discrete systems generated by given sequences of maps in metric spaces. In the case that the metric space is compact, it is shown that a system is Li-Yorke{\\delta}-chaotic if and only if it is distributionally{\\delta}'-chaotic in a sequence; and three criteria of distributional {\\delta}-chaos are established, which are caused by topologically weak mixing, asymptotic average shadowing property, and some expanding condition, respectively, where {\\delta} and {\\delta}' are positive constants. In a general case, a criterion of distributional"},"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":"1801.04445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-13T14:20:24Z","cross_cats_sorted":[],"title_canon_sha256":"5c932e13d93443f38c3d584d6e77832f7b87e2d9c7251364a4fe39baad48e4d6","abstract_canon_sha256":"d89a5f8c2d67e0127beabb0a8e07b20d0050f63ae88ad43403450111ce47c7da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:06.687145Z","signature_b64":"QadOVqMDhOT5GM9ZRtivM8PCv35RFez3HSSn8lsi2TqWdts89P8h3T9WZ1eyvRwNSHGCGPL9FvvuGjWSgGLuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"363b4dd2ebdfffc737c2fe4587fb2c989f7676e72ec5b3060a18bdc3d7216065","last_reissued_at":"2026-05-18T00:21:06.686524Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:06.686524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On distributional chaos in non-autonomous discrete systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hao Zhu, Hua Shao, Yuming Shi","submitted_at":"2018-01-13T14:20:24Z","abstract_excerpt":"This paper studies distributional chaos in non-autonomous discrete systems generated by given sequences of maps in metric spaces. In the case that the metric space is compact, it is shown that a system is Li-Yorke{\\delta}-chaotic if and only if it is distributionally{\\delta}'-chaotic in a sequence; and three criteria of distributional {\\delta}-chaos are established, which are caused by topologically weak mixing, asymptotic average shadowing property, and some expanding condition, respectively, where {\\delta} and {\\delta}' are positive constants. In a general case, a criterion of distributional"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04445","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":"1801.04445","created_at":"2026-05-18T00:21:06.686620+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.04445v1","created_at":"2026-05-18T00:21:06.686620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04445","created_at":"2026-05-18T00:21:06.686620+00:00"},{"alias_kind":"pith_short_12","alias_value":"GY5U3UXL3774","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GY5U3UXL3774ON6C","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GY5U3UXL","created_at":"2026-05-18T12:32:25.280505+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/GY5U3UXL3774ON6C7ZCYP6ZMTC","json":"https://pith.science/pith/GY5U3UXL3774ON6C7ZCYP6ZMTC.json","graph_json":"https://pith.science/api/pith-number/GY5U3UXL3774ON6C7ZCYP6ZMTC/graph.json","events_json":"https://pith.science/api/pith-number/GY5U3UXL3774ON6C7ZCYP6ZMTC/events.json","paper":"https://pith.science/paper/GY5U3UXL"},"agent_actions":{"view_html":"https://pith.science/pith/GY5U3UXL3774ON6C7ZCYP6ZMTC","download_json":"https://pith.science/pith/GY5U3UXL3774ON6C7ZCYP6ZMTC.json","view_paper":"https://pith.science/paper/GY5U3UXL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.04445&json=true","fetch_graph":"https://pith.science/api/pith-number/GY5U3UXL3774ON6C7ZCYP6ZMTC/graph.json","fetch_events":"https://pith.science/api/pith-number/GY5U3UXL3774ON6C7ZCYP6ZMTC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GY5U3UXL3774ON6C7ZCYP6ZMTC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GY5U3UXL3774ON6C7ZCYP6ZMTC/action/storage_attestation","attest_author":"https://pith.science/pith/GY5U3UXL3774ON6C7ZCYP6ZMTC/action/author_attestation","sign_citation":"https://pith.science/pith/GY5U3UXL3774ON6C7ZCYP6ZMTC/action/citation_signature","submit_replication":"https://pith.science/pith/GY5U3UXL3774ON6C7ZCYP6ZMTC/action/replication_record"}},"created_at":"2026-05-18T00:21:06.686620+00:00","updated_at":"2026-05-18T00:21:06.686620+00:00"}