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Equivalence of positive entropy and the existence of a large (in terms of asymptotic and Shnirelman densities) set of combinatorial independence for shift spaces.\n  2. Existence of a mixing shift space with a dense set of periodic points with topological entropy zero and without ergodic measure with full support, nor any distributionally chaotic pair.\n  Our proofs are new and yield conc"},"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":"1502.03981","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-13T13:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"0d76be3090f0307517d2ed5a84034ba84839ef7414d23b6d0f3d91be8cc32ade","abstract_canon_sha256":"8785c1f08ed58f3f580e8187ad13961e047f41f2876471108dae9e9061a24a55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:03.937804Z","signature_b64":"QPz/CPPptknAz+iUC90HcBtsIQvs1/gEs3lSxhZT0LCWXr/Z/wK1p8bOOQz3ACmVQAzPjUSok3d6B/hPJfL2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7172b375a21dd3201a6ed6218159a7d1d65c9f0ae445241c94178823d1e381ee","last_reissued_at":"2026-05-18T01:24:03.937132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:03.937132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two results on entropy, chaos, and independence in symbolic dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dominik Kwietniak, Fryderyk Falniowski, Jian Li, Marcin Kulczycki","submitted_at":"2015-02-13T13:39:08Z","abstract_excerpt":"We survey the connections between entropy, chaos, and independence in topological dynamics. 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