{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IJ3O2ZFBK2KN5NWAMHYWHO4QXY","short_pith_number":"pith:IJ3O2ZFB","schema_version":"1.0","canonical_sha256":"4276ed64a15694deb6c061f163bb90be3da47396e24ac3f957eeb075b52b0908","source":{"kind":"arxiv","id":"1608.02697","version":2},"attestation_state":"computed","paper":{"title":"M\\\"obius disjointness for non-uniquely ergodic skew products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Zhiren Wang","submitted_at":"2016-08-09T05:54:21Z","abstract_excerpt":"For $\\tau>2$, let $T$ be a $C^\\tau$ skew product map of the form $(x+\\alpha,y+h(x))$ on $\\mathbb T^2$ over a rotation of the circle. We show that if $T$ preserves a measurable section, then it is disjoint to the M\\\"{o}bius sequence. This in particular implies that any non-uniquely ergodic $C^\\tau$ skew product map on $\\mathbb T^2$ has a finite index factor that is disjoint to the M\\\"{o}bius sequence."},"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":"1608.02697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-09T05:54:21Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"2e7b8c521c2361d5991387656bc8eed04481b410275524cc64200066db234e37","abstract_canon_sha256":"ea421080e9692371ab091f1ae4099da330c1b97cdeae3c25304a379dd083f1ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:53.183108Z","signature_b64":"bPxht3UrGvQvU3QHzn66kOvX7V7AquB7kQXVRkgMb2S1OZBqrtsKk3D5oLCfq3KvhhNe7DwcS4+P7LJVS+hKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4276ed64a15694deb6c061f163bb90be3da47396e24ac3f957eeb075b52b0908","last_reissued_at":"2026-05-18T00:33:53.182572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:53.182572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"M\\\"obius disjointness for non-uniquely ergodic skew products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Zhiren Wang","submitted_at":"2016-08-09T05:54:21Z","abstract_excerpt":"For $\\tau>2$, let $T$ be a $C^\\tau$ skew product map of the form $(x+\\alpha,y+h(x))$ on $\\mathbb T^2$ over a rotation of the circle. We show that if $T$ preserves a measurable section, then it is disjoint to the M\\\"{o}bius sequence. This in particular implies that any non-uniquely ergodic $C^\\tau$ skew product map on $\\mathbb T^2$ has a finite index factor that is disjoint to the M\\\"{o}bius sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02697","kind":"arxiv","version":2},"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":"1608.02697","created_at":"2026-05-18T00:33:53.182665+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.02697v2","created_at":"2026-05-18T00:33:53.182665+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02697","created_at":"2026-05-18T00:33:53.182665+00:00"},{"alias_kind":"pith_short_12","alias_value":"IJ3O2ZFBK2KN","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IJ3O2ZFBK2KN5NWA","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IJ3O2ZFB","created_at":"2026-05-18T12:30:22.444734+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/IJ3O2ZFBK2KN5NWAMHYWHO4QXY","json":"https://pith.science/pith/IJ3O2ZFBK2KN5NWAMHYWHO4QXY.json","graph_json":"https://pith.science/api/pith-number/IJ3O2ZFBK2KN5NWAMHYWHO4QXY/graph.json","events_json":"https://pith.science/api/pith-number/IJ3O2ZFBK2KN5NWAMHYWHO4QXY/events.json","paper":"https://pith.science/paper/IJ3O2ZFB"},"agent_actions":{"view_html":"https://pith.science/pith/IJ3O2ZFBK2KN5NWAMHYWHO4QXY","download_json":"https://pith.science/pith/IJ3O2ZFBK2KN5NWAMHYWHO4QXY.json","view_paper":"https://pith.science/paper/IJ3O2ZFB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.02697&json=true","fetch_graph":"https://pith.science/api/pith-number/IJ3O2ZFBK2KN5NWAMHYWHO4QXY/graph.json","fetch_events":"https://pith.science/api/pith-number/IJ3O2ZFBK2KN5NWAMHYWHO4QXY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IJ3O2ZFBK2KN5NWAMHYWHO4QXY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IJ3O2ZFBK2KN5NWAMHYWHO4QXY/action/storage_attestation","attest_author":"https://pith.science/pith/IJ3O2ZFBK2KN5NWAMHYWHO4QXY/action/author_attestation","sign_citation":"https://pith.science/pith/IJ3O2ZFBK2KN5NWAMHYWHO4QXY/action/citation_signature","submit_replication":"https://pith.science/pith/IJ3O2ZFBK2KN5NWAMHYWHO4QXY/action/replication_record"}},"created_at":"2026-05-18T00:33:53.182665+00:00","updated_at":"2026-05-18T00:33:53.182665+00:00"}