{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:IXUUOKNNV2I2HG2VHNE6UYC4QU","short_pith_number":"pith:IXUUOKNN","schema_version":"1.0","canonical_sha256":"45e94729adae91a39b553b49ea605c85070dd21227e8d41d3d9156a6020a5304","source":{"kind":"arxiv","id":"1108.0714","version":3},"attestation_state":"computed","paper":{"title":"Open Saturated Sets Without Holonomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"John Cantwell, Lawrence Conlon","submitted_at":"2011-08-03T00:02:20Z","abstract_excerpt":"Open, connected, saturated sets W without holonomy in codimension one foliations play key roles as fundamental building blocks. Here, for the case of foliated 3-manifolds, we produce a finite system of closed, convex, non-overlapping polyhedral cones in the first cohomology of W with real coefficients such that the isotopy classes of possible foliations of W without holonomy, either dense leaved in W or proper, correspond one-to-one to the rays in the interiors of these cones. This generalizes our classification of depth one foliations to foliations of finite depth and more general foliations."},"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":"1108.0714","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-03T00:02:20Z","cross_cats_sorted":[],"title_canon_sha256":"9a05393199a4a2b6101270faff2548f9f93943f50b89384382e678eb12063a09","abstract_canon_sha256":"5c51e58590be8555abbcddb7fe5ed8877e5f25ed648573a5eadc7958c32430ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:14.694990Z","signature_b64":"iF/DJzJtsIoFRBIbwef0Wfr6dk7WotHGS1cmseseNi+U5NVweH8s56ObnKXOZqQN5iKPGgT14M8lyoUlF+/6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45e94729adae91a39b553b49ea605c85070dd21227e8d41d3d9156a6020a5304","last_reissued_at":"2026-05-18T01:19:14.694188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:14.694188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Open Saturated Sets Without Holonomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"John Cantwell, Lawrence Conlon","submitted_at":"2011-08-03T00:02:20Z","abstract_excerpt":"Open, connected, saturated sets W without holonomy in codimension one foliations play key roles as fundamental building blocks. Here, for the case of foliated 3-manifolds, we produce a finite system of closed, convex, non-overlapping polyhedral cones in the first cohomology of W with real coefficients such that the isotopy classes of possible foliations of W without holonomy, either dense leaved in W or proper, correspond one-to-one to the rays in the interiors of these cones. This generalizes our classification of depth one foliations to foliations of finite depth and more general foliations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0714","kind":"arxiv","version":3},"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":"1108.0714","created_at":"2026-05-18T01:19:14.694331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.0714v3","created_at":"2026-05-18T01:19:14.694331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0714","created_at":"2026-05-18T01:19:14.694331+00:00"},{"alias_kind":"pith_short_12","alias_value":"IXUUOKNNV2I2","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"IXUUOKNNV2I2HG2V","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"IXUUOKNN","created_at":"2026-05-18T12:26:32.869790+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/IXUUOKNNV2I2HG2VHNE6UYC4QU","json":"https://pith.science/pith/IXUUOKNNV2I2HG2VHNE6UYC4QU.json","graph_json":"https://pith.science/api/pith-number/IXUUOKNNV2I2HG2VHNE6UYC4QU/graph.json","events_json":"https://pith.science/api/pith-number/IXUUOKNNV2I2HG2VHNE6UYC4QU/events.json","paper":"https://pith.science/paper/IXUUOKNN"},"agent_actions":{"view_html":"https://pith.science/pith/IXUUOKNNV2I2HG2VHNE6UYC4QU","download_json":"https://pith.science/pith/IXUUOKNNV2I2HG2VHNE6UYC4QU.json","view_paper":"https://pith.science/paper/IXUUOKNN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.0714&json=true","fetch_graph":"https://pith.science/api/pith-number/IXUUOKNNV2I2HG2VHNE6UYC4QU/graph.json","fetch_events":"https://pith.science/api/pith-number/IXUUOKNNV2I2HG2VHNE6UYC4QU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IXUUOKNNV2I2HG2VHNE6UYC4QU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IXUUOKNNV2I2HG2VHNE6UYC4QU/action/storage_attestation","attest_author":"https://pith.science/pith/IXUUOKNNV2I2HG2VHNE6UYC4QU/action/author_attestation","sign_citation":"https://pith.science/pith/IXUUOKNNV2I2HG2VHNE6UYC4QU/action/citation_signature","submit_replication":"https://pith.science/pith/IXUUOKNNV2I2HG2VHNE6UYC4QU/action/replication_record"}},"created_at":"2026-05-18T01:19:14.694331+00:00","updated_at":"2026-05-18T01:19:14.694331+00:00"}