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Moreover, for every fixed $k\\in \\N$, the set $\\{n\\in \\N:\\,k\\nmid m_n \\}$ is infinite.\n  This is a sufficient condition for the existence of a rigid, weakly mixing dynamical system whose rigidity time is not a rigidity time for any system with a discrete part in its spectrum."},"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":"1406.7518","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-29T15:43:03Z","cross_cats_sorted":[],"title_canon_sha256":"c7c20b03046f8e7a9989b81056b2dc37517f3b35aed9d7f67e5ddae6af5b1781","abstract_canon_sha256":"d4e2e2011765998860d2ab0da3d11ed39610bbaca53a8cbbb0c82dfc5244bb68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:45.081434Z","signature_b64":"UxYDT5RKLFAl6QUyG+9n0vY0NOGoHnrLnxEYPqneu3DY5DZ70JXKJhL9ctSSqA5Fs1Rn9Jnfbtt4rok5jrGtBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14807bf3fddc3fd0cdfcd09dd0dea12f4309c9b8c3ddefd30a037dc4b6010d9d","last_reissued_at":"2026-05-18T02:48:45.080749Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:45.080749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity times for weakly mixing dynamical system which are not rigidity times for any irrational rotation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adam Kanigowski, Bassam Fayad","submitted_at":"2014-06-29T15:43:03Z","abstract_excerpt":"We construct an increasing sequence of natural numbers $(m_n)_{n=1}^{+\\infty}$ with the property that $(m_n \\th [1])_{n\\geq 1}$ is dense in $\\T$ for any $\\th \\in \\R\\setminus \\Q$, and a continuous measure on the circle $\\mu$ such that $\\lim_{n\\to +\\infty}\\int_{\\T}\\|m_n\\theta\\|d\\mu(\\theta)=0$. Moreover, for every fixed $k\\in \\N$, the set $\\{n\\in \\N:\\,k\\nmid m_n \\}$ is infinite.\n  This is a sufficient condition for the existence of a rigid, weakly mixing dynamical system whose rigidity time is not a rigidity time for any system with a discrete part in its spectrum."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7518","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":"1406.7518","created_at":"2026-05-18T02:48:45.080839+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.7518v1","created_at":"2026-05-18T02:48:45.080839+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7518","created_at":"2026-05-18T02:48:45.080839+00:00"},{"alias_kind":"pith_short_12","alias_value":"CSAHX4753Q75","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CSAHX4753Q75BTP4","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CSAHX475","created_at":"2026-05-18T12:28:22.404517+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/CSAHX4753Q75BTP42CO5BXVBF5","json":"https://pith.science/pith/CSAHX4753Q75BTP42CO5BXVBF5.json","graph_json":"https://pith.science/api/pith-number/CSAHX4753Q75BTP42CO5BXVBF5/graph.json","events_json":"https://pith.science/api/pith-number/CSAHX4753Q75BTP42CO5BXVBF5/events.json","paper":"https://pith.science/paper/CSAHX475"},"agent_actions":{"view_html":"https://pith.science/pith/CSAHX4753Q75BTP42CO5BXVBF5","download_json":"https://pith.science/pith/CSAHX4753Q75BTP42CO5BXVBF5.json","view_paper":"https://pith.science/paper/CSAHX475","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.7518&json=true","fetch_graph":"https://pith.science/api/pith-number/CSAHX4753Q75BTP42CO5BXVBF5/graph.json","fetch_events":"https://pith.science/api/pith-number/CSAHX4753Q75BTP42CO5BXVBF5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CSAHX4753Q75BTP42CO5BXVBF5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CSAHX4753Q75BTP42CO5BXVBF5/action/storage_attestation","attest_author":"https://pith.science/pith/CSAHX4753Q75BTP42CO5BXVBF5/action/author_attestation","sign_citation":"https://pith.science/pith/CSAHX4753Q75BTP42CO5BXVBF5/action/citation_signature","submit_replication":"https://pith.science/pith/CSAHX4753Q75BTP42CO5BXVBF5/action/replication_record"}},"created_at":"2026-05-18T02:48:45.080839+00:00","updated_at":"2026-05-18T02:48:45.080839+00:00"}