{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:R4PM6I35SAX2XG2USR2NVFVBE5","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":"c5efb8ccc93c7e261888b87b6de910b5b6b72d7a6c9303c5a07ba335340353b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-27T04:44:24Z","title_canon_sha256":"b035436315fbca5713d07a171de7e6039e14be855364a01e2dd963cd250636c1"},"schema_version":"1.0","source":{"id":"1410.7118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7118","created_at":"2026-05-18T01:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7118v1","created_at":"2026-05-18T01:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7118","created_at":"2026-05-18T01:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"R4PM6I35SAX2","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R4PM6I35SAX2XG2U","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R4PM6I35","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:c41265d1d558f7618fc126bf5d22491530ef8057a54c4e532d7c0f38e14be1ab","target":"graph","created_at":"2026-05-18T01:13:16Z","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":"We show that for a non-trivial transitive dynamical system, it has a dense Mycielski invariant strongly scrambled set if and only if it has a fixed point, and it has a dense Mycielski invariant $\\delta$-scrambled set for some $\\delta>0$ if and only if it has a fixed point and not uniformly rigid. We also provide two methods for the construction of completely scrambled systems which are weakly mixing, proximal and uniformly rigid.","authors_text":"Jian Li, Magdalena Fory\\'s, Piotr Oprocha, Wen Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-27T04:44:24Z","title":"Invariant scrambled sets, uniform rigidity and weak mixing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7118","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:e446745e91510864cd2963d5754a1067ae1b5d1ea2df3a0d848cb176cf901a66","target":"record","created_at":"2026-05-18T01:13:16Z","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":"c5efb8ccc93c7e261888b87b6de910b5b6b72d7a6c9303c5a07ba335340353b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-27T04:44:24Z","title_canon_sha256":"b035436315fbca5713d07a171de7e6039e14be855364a01e2dd963cd250636c1"},"schema_version":"1.0","source":{"id":"1410.7118","kind":"arxiv","version":1}},"canonical_sha256":"8f1ecf237d902fab9b549474da96a12774338101653c0519e71116773a556b0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f1ecf237d902fab9b549474da96a12774338101653c0519e71116773a556b0f","first_computed_at":"2026-05-18T01:13:16.970198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:16.970198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cpaGNtg6A/uVmTyyRje2yJ/4D9fUr+bOgUXsYJQYDCPq/GDZrVixSv9aprFh5QIJHI5sIn2DWdYS5cIl3SVHDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:16.970697Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e446745e91510864cd2963d5754a1067ae1b5d1ea2df3a0d848cb176cf901a66","sha256:c41265d1d558f7618fc126bf5d22491530ef8057a54c4e532d7c0f38e14be1ab"],"state_sha256":"18398b29d9fd801b1830036d9700eb4401844b49771a372add63f964e206a07a"}