{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:USMSR55MCYNVUOHRANC3W54XSP","short_pith_number":"pith:USMSR55M","schema_version":"1.0","canonical_sha256":"a49928f7ac161b5a38f10345bb779793f5191d89078d61e80fa81bf935c1ed48","source":{"kind":"arxiv","id":"1904.09826","version":1},"attestation_state":"computed","paper":{"title":"Invariance of distributional chaos for backward shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Xinxing Wu, Yang Luo","submitted_at":"2019-04-22T12:37:46Z","abstract_excerpt":"A sufficient and necessary condition ensuring that the backward shift operator on the K\\\"{o}the sequence space admits an invariant distributionally $\\varepsilon$-scrambled set for some $\\varepsilon>0$ is obtained, improving the main results in [F. Mart\\'{\\i}nez-Gim\\'{e}nez, P. Oprocha, A. Peris, J. Math. Anal. Appl., {\\bf 351} (2009), 607--615]."},"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":"1904.09826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-22T12:37:46Z","cross_cats_sorted":[],"title_canon_sha256":"9cac02b6c553abdccc13adfd7544a9c549bd6880d3e3d32ab53ee976e1547c8b","abstract_canon_sha256":"7c4fd7fbd0ea3e7f5d5287849d3a46d0465f0a8b9a1bae08daca6792b6e7b201"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:03.165056Z","signature_b64":"BMiYdxYtiZCofSCMFjg8U5QyjfRFYzuvd49gAX5Rt6BSXR4sgN5bibe0dWHkxD/+TUIbmPJg49P/8zVyTFfyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a49928f7ac161b5a38f10345bb779793f5191d89078d61e80fa81bf935c1ed48","last_reissued_at":"2026-05-17T23:48:03.164200Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:03.164200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariance of distributional chaos for backward shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Xinxing Wu, Yang Luo","submitted_at":"2019-04-22T12:37:46Z","abstract_excerpt":"A sufficient and necessary condition ensuring that the backward shift operator on the K\\\"{o}the sequence space admits an invariant distributionally $\\varepsilon$-scrambled set for some $\\varepsilon>0$ is obtained, improving the main results in [F. Mart\\'{\\i}nez-Gim\\'{e}nez, P. Oprocha, A. Peris, J. Math. Anal. Appl., {\\bf 351} (2009), 607--615]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09826","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":"1904.09826","created_at":"2026-05-17T23:48:03.164350+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.09826v1","created_at":"2026-05-17T23:48:03.164350+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09826","created_at":"2026-05-17T23:48:03.164350+00:00"},{"alias_kind":"pith_short_12","alias_value":"USMSR55MCYNV","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"USMSR55MCYNVUOHR","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"USMSR55M","created_at":"2026-05-18T12:33:30.264802+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/USMSR55MCYNVUOHRANC3W54XSP","json":"https://pith.science/pith/USMSR55MCYNVUOHRANC3W54XSP.json","graph_json":"https://pith.science/api/pith-number/USMSR55MCYNVUOHRANC3W54XSP/graph.json","events_json":"https://pith.science/api/pith-number/USMSR55MCYNVUOHRANC3W54XSP/events.json","paper":"https://pith.science/paper/USMSR55M"},"agent_actions":{"view_html":"https://pith.science/pith/USMSR55MCYNVUOHRANC3W54XSP","download_json":"https://pith.science/pith/USMSR55MCYNVUOHRANC3W54XSP.json","view_paper":"https://pith.science/paper/USMSR55M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.09826&json=true","fetch_graph":"https://pith.science/api/pith-number/USMSR55MCYNVUOHRANC3W54XSP/graph.json","fetch_events":"https://pith.science/api/pith-number/USMSR55MCYNVUOHRANC3W54XSP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/USMSR55MCYNVUOHRANC3W54XSP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/USMSR55MCYNVUOHRANC3W54XSP/action/storage_attestation","attest_author":"https://pith.science/pith/USMSR55MCYNVUOHRANC3W54XSP/action/author_attestation","sign_citation":"https://pith.science/pith/USMSR55MCYNVUOHRANC3W54XSP/action/citation_signature","submit_replication":"https://pith.science/pith/USMSR55MCYNVUOHRANC3W54XSP/action/replication_record"}},"created_at":"2026-05-17T23:48:03.164350+00:00","updated_at":"2026-05-17T23:48:03.164350+00:00"}