{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7JE3BHYQQVXSBYJPPJ7UTLRRDG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7402b5d8bd789aee96b6234f6c1d2d7de2e2bd0e5dda5500520cf9165f493e15","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-20T02:21:18Z","title_canon_sha256":"29379087756cfc56f2138101c08548321b458a950c77502e22cfac585e159474"},"schema_version":"1.0","source":{"id":"1707.06345","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06345","created_at":"2026-05-18T00:39:54Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06345v1","created_at":"2026-05-18T00:39:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06345","created_at":"2026-05-18T00:39:54Z"},{"alias_kind":"pith_short_12","alias_value":"7JE3BHYQQVXS","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7JE3BHYQQVXSBYJP","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7JE3BHYQ","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:d0815f26b7a746454caf7b928a1640d03958d8e966b9c53517f139ea3ea61a99","target":"graph","created_at":"2026-05-18T00:39:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, the notion of measure complexity is introduced for a topological dynamical system and it is shown that Sarnak's M\\\"{o}bius disjointness conjecture holds for any system for which every invariant Borel probability measure has sub-polynomial measure complexity.\n  Moreover, it is proved that the following classes of topological dynamical systems $(X,T)$ meet this condition and hence satisfy Sarnak's conjecture: (1) Each invariant Borel probability measure of $T$ has discrete spectrum. (2) $T$ is a homotopically trivial $C^\\infty$ skew product system on $\\mathbb{T}^2$ over an irratio","authors_text":"Wen Huang, Xiangdong Ye, Zhiren Wang","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-20T02:21:18Z","title":"Measure complexity and M\\\"obius disjointness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06345","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e4853a5aa14512b7ebdb70b9047769d79a832d94bcc0350d795b3081e7daffca","target":"record","created_at":"2026-05-18T00:39:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7402b5d8bd789aee96b6234f6c1d2d7de2e2bd0e5dda5500520cf9165f493e15","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-07-20T02:21:18Z","title_canon_sha256":"29379087756cfc56f2138101c08548321b458a950c77502e22cfac585e159474"},"schema_version":"1.0","source":{"id":"1707.06345","kind":"arxiv","version":1}},"canonical_sha256":"fa49b09f10856f20e12f7a7f49ae3119ada689e908b4ec01f01f6be226706293","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa49b09f10856f20e12f7a7f49ae3119ada689e908b4ec01f01f6be226706293","first_computed_at":"2026-05-18T00:39:54.078920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:54.078920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CC2OjqXDUVa5WRGJ4QdIiaKPfmddzfRKVvNE9xpFu51aWVfZ5MPoqK9zFU1M/7G94+/l/ykrnmSvyFuytaHiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:54.079594Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06345","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4853a5aa14512b7ebdb70b9047769d79a832d94bcc0350d795b3081e7daffca","sha256:d0815f26b7a746454caf7b928a1640d03958d8e966b9c53517f139ea3ea61a99"],"state_sha256":"22912c0914428af84ba279f38a878c825a6e388fe48ccf06715b83379faa2f4b"}