{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:53I2VCPI4IS4YLR5B6LNS72FPR","short_pith_number":"pith:53I2VCPI","schema_version":"1.0","canonical_sha256":"eed1aa89e8e225cc2e3d0f96d97f457c6812f5b9ccc1ddfed47f8fbe17099c5e","source":{"kind":"arxiv","id":"1310.2546","version":2},"attestation_state":"computed","paper":{"title":"The Moebius function and continuous extensions of rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Joanna Ku{\\l}aga-Przymus, Mariusz Lema\\'nczyk","submitted_at":"2013-10-09T17:06:29Z","abstract_excerpt":"Let $f\\colon \\mathbb{T}\\to \\mathbb{R}$ be of class $C^{1+\\delta}$ for some $\\delta>0$ and let $c\\in\\mathbb{Z}$. We show that for a generic $\\alpha\\in\\mathbb{R}$, the extension $T_{c,f}\\colon \\mathbb{T}^2\\to\\mathbb{T}^2$ of the irrational rotation $Tx=x+\\alpha$, given by $T_{c,f}(x,u)=(x+\\alpha, u+cx+f(x))$ ($\\bmod\\ 1$) satisfies Sarnak's conjecture."},"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":"1310.2546","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-09T17:06:29Z","cross_cats_sorted":[],"title_canon_sha256":"d0f96ad72081283bfb669d0e63e31a07342e790aaed578ca6600bf638a7b264e","abstract_canon_sha256":"c1039af22711391bfe786e5e0cafb07fd735ffe32fad31cf109749ff208c4db3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:55.897205Z","signature_b64":"s2Qi39rO2j8WoS/JnjVu2elZnxxzXaxrXEaBQ87LedZFPN1raVlGtmp0WSc/bc7zkUw/NrpD/kmjlU+rfqrxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eed1aa89e8e225cc2e3d0f96d97f457c6812f5b9ccc1ddfed47f8fbe17099c5e","last_reissued_at":"2026-05-18T02:45:55.896524Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:55.896524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Moebius function and continuous extensions of rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Joanna Ku{\\l}aga-Przymus, Mariusz Lema\\'nczyk","submitted_at":"2013-10-09T17:06:29Z","abstract_excerpt":"Let $f\\colon \\mathbb{T}\\to \\mathbb{R}$ be of class $C^{1+\\delta}$ for some $\\delta>0$ and let $c\\in\\mathbb{Z}$. We show that for a generic $\\alpha\\in\\mathbb{R}$, the extension $T_{c,f}\\colon \\mathbb{T}^2\\to\\mathbb{T}^2$ of the irrational rotation $Tx=x+\\alpha$, given by $T_{c,f}(x,u)=(x+\\alpha, u+cx+f(x))$ ($\\bmod\\ 1$) satisfies Sarnak's conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2546","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":"1310.2546","created_at":"2026-05-18T02:45:55.896611+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.2546v2","created_at":"2026-05-18T02:45:55.896611+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2546","created_at":"2026-05-18T02:45:55.896611+00:00"},{"alias_kind":"pith_short_12","alias_value":"53I2VCPI4IS4","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"53I2VCPI4IS4YLR5","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"53I2VCPI","created_at":"2026-05-18T12:27:34.582898+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/53I2VCPI4IS4YLR5B6LNS72FPR","json":"https://pith.science/pith/53I2VCPI4IS4YLR5B6LNS72FPR.json","graph_json":"https://pith.science/api/pith-number/53I2VCPI4IS4YLR5B6LNS72FPR/graph.json","events_json":"https://pith.science/api/pith-number/53I2VCPI4IS4YLR5B6LNS72FPR/events.json","paper":"https://pith.science/paper/53I2VCPI"},"agent_actions":{"view_html":"https://pith.science/pith/53I2VCPI4IS4YLR5B6LNS72FPR","download_json":"https://pith.science/pith/53I2VCPI4IS4YLR5B6LNS72FPR.json","view_paper":"https://pith.science/paper/53I2VCPI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.2546&json=true","fetch_graph":"https://pith.science/api/pith-number/53I2VCPI4IS4YLR5B6LNS72FPR/graph.json","fetch_events":"https://pith.science/api/pith-number/53I2VCPI4IS4YLR5B6LNS72FPR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/53I2VCPI4IS4YLR5B6LNS72FPR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/53I2VCPI4IS4YLR5B6LNS72FPR/action/storage_attestation","attest_author":"https://pith.science/pith/53I2VCPI4IS4YLR5B6LNS72FPR/action/author_attestation","sign_citation":"https://pith.science/pith/53I2VCPI4IS4YLR5B6LNS72FPR/action/citation_signature","submit_replication":"https://pith.science/pith/53I2VCPI4IS4YLR5B6LNS72FPR/action/replication_record"}},"created_at":"2026-05-18T02:45:55.896611+00:00","updated_at":"2026-05-18T02:45:55.896611+00:00"}