{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:USMSR55MCYNVUOHRANC3W54XSP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7c4fd7fbd0ea3e7f5d5287849d3a46d0465f0a8b9a1bae08daca6792b6e7b201","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-22T12:37:46Z","title_canon_sha256":"9cac02b6c553abdccc13adfd7544a9c549bd6880d3e3d32ab53ee976e1547c8b"},"schema_version":"1.0","source":{"id":"1904.09826","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.09826","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"1904.09826v1","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09826","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"USMSR55MCYNV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"USMSR55MCYNVUOHR","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"USMSR55M","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:e8a7993e58d9b4590e9c7e4766e20a70c6a50e1cd9f5ac046c0157b04ece22d0","target":"graph","created_at":"2026-05-17T23:48:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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].","authors_text":"Xinxing Wu, Yang Luo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-22T12:37:46Z","title":"Invariance of distributional chaos for backward shifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09826","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:959a832d3c2917a2c870599f33b884282ee94e5555d001021de61d726f9591c6","target":"record","created_at":"2026-05-17T23:48:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7c4fd7fbd0ea3e7f5d5287849d3a46d0465f0a8b9a1bae08daca6792b6e7b201","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-04-22T12:37:46Z","title_canon_sha256":"9cac02b6c553abdccc13adfd7544a9c549bd6880d3e3d32ab53ee976e1547c8b"},"schema_version":"1.0","source":{"id":"1904.09826","kind":"arxiv","version":1}},"canonical_sha256":"a49928f7ac161b5a38f10345bb779793f5191d89078d61e80fa81bf935c1ed48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a49928f7ac161b5a38f10345bb779793f5191d89078d61e80fa81bf935c1ed48","first_computed_at":"2026-05-17T23:48:03.164200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:03.164200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BMiYdxYtiZCofSCMFjg8U5QyjfRFYzuvd49gAX5Rt6BSXR4sgN5bibe0dWHkxD/+TUIbmPJg49P/8zVyTFfyCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:03.165056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.09826","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:959a832d3c2917a2c870599f33b884282ee94e5555d001021de61d726f9591c6","sha256:e8a7993e58d9b4590e9c7e4766e20a70c6a50e1cd9f5ac046c0157b04ece22d0"],"state_sha256":"7c498e508c9b6c58091460e41691e5f8e9c702d396766462c723bde876e8c53e"}