{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WAQ7FAX5PXU4BEJWDUZM5OC2GP","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":"c133d820af6e42ac08352e92f023870524ffef30c601654df94bda68476a1989","cross_cats_sorted":["math.CV","math.DG","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-01T09:21:07Z","title_canon_sha256":"9107f7358d14a00eb410c8fa3e093e01253841b23aaf65c177036f0f07107a42"},"schema_version":"1.0","source":{"id":"1708.00216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00216","created_at":"2026-05-18T00:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00216v1","created_at":"2026-05-18T00:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00216","created_at":"2026-05-18T00:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"WAQ7FAX5PXU4","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WAQ7FAX5PXU4BEJW","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WAQ7FAX5","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:a659f8f54f3b411aaf13795b65e4e2ffb6e4b9fc60a45ddda987701882acffb0","target":"graph","created_at":"2026-05-18T00:32:35Z","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":"Let $Z$ be a non-compact two-dimensional manifold obtained from a family of open strips $\\mathbb{R}\\times(0,1)$ with boundary intervals by gluing those strips along their boundary intervals. Every such strip has a foliation into parallel lines $\\mathbb{R}\\times t$, $t\\in(0,1)$, and boundary intervals, whence we get a foliation $\\Delta$ on all of $Z$. Many types of foliations on surfaces with leaves homeomorphic to the real line have such \"striped\" structure. That fact was discovered by W. Kaplan (1940-41) for foliations on the plane $\\mathbb{R}^2$ by level-set of pseudo-harmonic functions $\\ma","authors_text":"Eugene Polulyakh, Sergiy Maksymenko, Yuliya Soroka","cross_cats":["math.CV","math.DG","math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-01T09:21:07Z","title":"Homeotopy groups of one-dimensional foliations on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00216","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:c1e63a3eaa2a40c90a73618e1d19f757118363f46116c1486b263650fa867422","target":"record","created_at":"2026-05-18T00:32:35Z","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":"c133d820af6e42ac08352e92f023870524ffef30c601654df94bda68476a1989","cross_cats_sorted":["math.CV","math.DG","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-01T09:21:07Z","title_canon_sha256":"9107f7358d14a00eb410c8fa3e093e01253841b23aaf65c177036f0f07107a42"},"schema_version":"1.0","source":{"id":"1708.00216","kind":"arxiv","version":1}},"canonical_sha256":"b021f282fd7de9c091361d32ceb85a33c137e78aea923b877d287ff441492385","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b021f282fd7de9c091361d32ceb85a33c137e78aea923b877d287ff441492385","first_computed_at":"2026-05-18T00:32:35.990530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:35.990530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Chm/7p9dod2gCL3t9bD81SNSI1xvSiIUKvLV9JntKSzSOJVz7/BUJlmWK7GwwnfgUQnNAw1/0e64YW0a/o3Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:35.992151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1e63a3eaa2a40c90a73618e1d19f757118363f46116c1486b263650fa867422","sha256:a659f8f54f3b411aaf13795b65e4e2ffb6e4b9fc60a45ddda987701882acffb0"],"state_sha256":"c9f6b188d9e33dbd74b85e9e7c5a3becb9c1052ab68bfd013200f647d9816c53"}