{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GM2XLYP4UIAJFCVVXMQ3VVBMMH","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":"bd8e494f048a3560907c4f06ab6fa41ab27a867ac8e61f3b621e54930112697e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-11-06T03:54:18Z","title_canon_sha256":"a8a3e1252bdceae137e2af5094ae551bc7f738773664d3910202829e650d3cab"},"schema_version":"1.0","source":{"id":"1711.01716","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01716","created_at":"2026-05-18T00:30:21Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01716v2","created_at":"2026-05-18T00:30:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01716","created_at":"2026-05-18T00:30:21Z"},{"alias_kind":"pith_short_12","alias_value":"GM2XLYP4UIAJ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GM2XLYP4UIAJFCVV","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GM2XLYP4","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:474e78a975f285dc1de7176f1f00ef7a19dd3f331f778cb69e5546aca8c7fc48","target":"graph","created_at":"2026-05-18T00:30:21Z","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":"This article is a survey of the Novikov problem of the structure of leaves of the foliations induced by a collection of closed 1-forms in a compact manifold $M$. Equivalently, this is to the study of the level sets of multivalued functions on $M$. To date, this problem was thoroughly investigated only for $M=\\Bbb T^n$ and multivalued maps $F:\\Bbb T^n\\to\\Bbb R^{n-1}$ in three different particular cases: when all components of $F$ but one are multivalued, started by Novikov in 1981, when all components of $F$ but one are singlevalued, started by Zorich in 1994, when none of the components is sin","authors_text":"Roberto De Leo","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-11-06T03:54:18Z","title":"A survey on quasiperiodic topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01716","kind":"arxiv","version":2},"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":"sha256:9be2665d83355ce13837fc6bcbe98eb6ee7c4b31584d8217388f16773a99abd7","target":"record","created_at":"2026-05-18T00:30:21Z","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":"bd8e494f048a3560907c4f06ab6fa41ab27a867ac8e61f3b621e54930112697e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-11-06T03:54:18Z","title_canon_sha256":"a8a3e1252bdceae137e2af5094ae551bc7f738773664d3910202829e650d3cab"},"schema_version":"1.0","source":{"id":"1711.01716","kind":"arxiv","version":2}},"canonical_sha256":"333575e1fca200928ab5bb21bad42c61f040590504834cf82c832e54f8e3f70c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"333575e1fca200928ab5bb21bad42c61f040590504834cf82c832e54f8e3f70c","first_computed_at":"2026-05-18T00:30:21.766708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:21.766708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JAAH/DgvoGk5tI5JmO9J2zsHkmr6J+TOYQwIBLUbJJK7/i+dARxA6K3m0JPEQredpJEKHCPGBvkMJ7OD6IhmDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:21.767428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.01716","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9be2665d83355ce13837fc6bcbe98eb6ee7c4b31584d8217388f16773a99abd7","sha256:474e78a975f285dc1de7176f1f00ef7a19dd3f331f778cb69e5546aca8c7fc48"],"state_sha256":"c04ea6a9effff860831c8a1a6e187f4bd6191deae6765dc732a9aa7818c6d1a5"}