{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:COFONI23OHUZL2JIXCEDM7D5YW","short_pith_number":"pith:COFONI23","schema_version":"1.0","canonical_sha256":"138ae6a35b71e995e928b888367c7dc5874a34737f8cb0a4771251eb5f9c5ec4","source":{"kind":"arxiv","id":"1302.3075","version":1},"attestation_state":"computed","paper":{"title":"Remarks on step cocycles over rotations, centralizers and coboundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jean-Pierre Conze (IRMAR), Jonathan Marco (IRMAR)","submitted_at":"2013-02-13T13:18:52Z","abstract_excerpt":"By using a cocycle generated by the step function $\\varphi_{\\beta, \\gamma} = 1_{[0, \\beta]} - 1_{[0, \\beta]} (. + \\gamma)$ over an irrational rotation $x \\to x + \\alpha \\mod 1$, we present examples which illustrate different aspects of the general theory of cylinder maps. In particular, we construct non ergodic cocycles with ergodic compact quotients, cocycles generating an extension $T_{\\alpha, \\varphi}$ with a small centralizer. The constructions are related to diophantine properties of $\\alpha, \\beta, \\gamma$."},"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":"1302.3075","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-13T13:18:52Z","cross_cats_sorted":[],"title_canon_sha256":"6b26355e10e29451c67a270403f5ea0484cf4c3e70d1e090dbe89af2e6ea28d6","abstract_canon_sha256":"7d53571e6fcc3979b94793c6e112563587912a6247f3db96c76a651f7d9fffc3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:48.822093Z","signature_b64":"n1daJjsSdaFiv+/VOm1fJBf6pw15zzEtsGsIPjMH09Kqp8OOQ5LImkXEEJrcKwKa0zzrUf5rGV5NZ9kCZ1WwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"138ae6a35b71e995e928b888367c7dc5874a34737f8cb0a4771251eb5f9c5ec4","last_reissued_at":"2026-05-18T03:33:48.821406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:48.821406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on step cocycles over rotations, centralizers and coboundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jean-Pierre Conze (IRMAR), Jonathan Marco (IRMAR)","submitted_at":"2013-02-13T13:18:52Z","abstract_excerpt":"By using a cocycle generated by the step function $\\varphi_{\\beta, \\gamma} = 1_{[0, \\beta]} - 1_{[0, \\beta]} (. + \\gamma)$ over an irrational rotation $x \\to x + \\alpha \\mod 1$, we present examples which illustrate different aspects of the general theory of cylinder maps. In particular, we construct non ergodic cocycles with ergodic compact quotients, cocycles generating an extension $T_{\\alpha, \\varphi}$ with a small centralizer. The constructions are related to diophantine properties of $\\alpha, \\beta, \\gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3075","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":"1302.3075","created_at":"2026-05-18T03:33:48.821501+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.3075v1","created_at":"2026-05-18T03:33:48.821501+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3075","created_at":"2026-05-18T03:33:48.821501+00:00"},{"alias_kind":"pith_short_12","alias_value":"COFONI23OHUZ","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"COFONI23OHUZL2JI","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"COFONI23","created_at":"2026-05-18T12:27:40.988391+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/COFONI23OHUZL2JIXCEDM7D5YW","json":"https://pith.science/pith/COFONI23OHUZL2JIXCEDM7D5YW.json","graph_json":"https://pith.science/api/pith-number/COFONI23OHUZL2JIXCEDM7D5YW/graph.json","events_json":"https://pith.science/api/pith-number/COFONI23OHUZL2JIXCEDM7D5YW/events.json","paper":"https://pith.science/paper/COFONI23"},"agent_actions":{"view_html":"https://pith.science/pith/COFONI23OHUZL2JIXCEDM7D5YW","download_json":"https://pith.science/pith/COFONI23OHUZL2JIXCEDM7D5YW.json","view_paper":"https://pith.science/paper/COFONI23","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.3075&json=true","fetch_graph":"https://pith.science/api/pith-number/COFONI23OHUZL2JIXCEDM7D5YW/graph.json","fetch_events":"https://pith.science/api/pith-number/COFONI23OHUZL2JIXCEDM7D5YW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/COFONI23OHUZL2JIXCEDM7D5YW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/COFONI23OHUZL2JIXCEDM7D5YW/action/storage_attestation","attest_author":"https://pith.science/pith/COFONI23OHUZL2JIXCEDM7D5YW/action/author_attestation","sign_citation":"https://pith.science/pith/COFONI23OHUZL2JIXCEDM7D5YW/action/citation_signature","submit_replication":"https://pith.science/pith/COFONI23OHUZL2JIXCEDM7D5YW/action/replication_record"}},"created_at":"2026-05-18T03:33:48.821501+00:00","updated_at":"2026-05-18T03:33:48.821501+00:00"}