{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SDYDSWGN3LVLXGIXE32CIIEC5Y","short_pith_number":"pith:SDYDSWGN","canonical_record":{"source":{"id":"1610.00615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-03T16:15:11Z","cross_cats_sorted":["math.DG","math.DS","math.GN"],"title_canon_sha256":"afc08325403a2d61397e96e2eabfb140a9f8ca81b5afe7320936822058c761e3","abstract_canon_sha256":"c26cd9dbd0438ef27116a96616382a97e8ecd92a0c205416fb781549b7e25e18"},"schema_version":"1.0"},"canonical_sha256":"90f03958cddaeabb991726f4242082ee053a27a4152fd1bae570289f8e87aedd","source":{"kind":"arxiv","id":"1610.00615","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00615","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00615v1","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00615","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"SDYDSWGN3LVL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SDYDSWGN3LVLXGIX","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SDYDSWGN","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SDYDSWGN3LVLXGIXE32CIIEC5Y","target":"record","payload":{"canonical_record":{"source":{"id":"1610.00615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-03T16:15:11Z","cross_cats_sorted":["math.DG","math.DS","math.GN"],"title_canon_sha256":"afc08325403a2d61397e96e2eabfb140a9f8ca81b5afe7320936822058c761e3","abstract_canon_sha256":"c26cd9dbd0438ef27116a96616382a97e8ecd92a0c205416fb781549b7e25e18"},"schema_version":"1.0"},"canonical_sha256":"90f03958cddaeabb991726f4242082ee053a27a4152fd1bae570289f8e87aedd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:36.414461Z","signature_b64":"oSHykbHkBWkdDkpsFLxyS9z3AcI/k+UMrGRixd7VNGiSgTIKDzSRulnC0nzvAvDdIVXX8pCrImWcVoHw81fPAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90f03958cddaeabb991726f4242082ee053a27a4152fd1bae570289f8e87aedd","last_reissued_at":"2026-05-18T00:32:36.413830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:36.413830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.00615","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z/tWmwPbDCksF+dAlSwJDV0JGMwt/6o+VTrsZF1wp0//isG9K7fpitAEgKOk0+i5QCuGC4a5CGI/7JUZMOSJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:53:29.996413Z"},"content_sha256":"90a2326dcf0a7f6097e1d582351ac176c6cb69e885c05ca81707e00613ddb209","schema_version":"1.0","event_id":"sha256:90a2326dcf0a7f6097e1d582351ac176c6cb69e885c05ca81707e00613ddb209"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SDYDSWGN3LVLXGIXE32CIIEC5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One-dimensional foliations on topological manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.DS","math.GN"],"primary_cat":"math.GT","authors_text":"Eugene Polulyakh, Sergiy Maksymenko","submitted_at":"2016-10-03T16:15:11Z","abstract_excerpt":"Let $X$ be an $(n+1)$-dimensional manifold, $\\Delta$ be a one-dimensional foliation on $X$, and $p: X \\to X / \\Delta$ be a quotient map. We will say that a leaf $\\omega$ of $\\Delta$ is special whenever the space of leaves $X / \\Delta$ is not Hausdorff at $\\omega$. We present necessary and sufficient conditions for the map $p: X \\to X / \\Delta$ to be a locally trivial fibration under assumptions that all leaves of $\\Delta$ are non-compact and the family of all special leaves of $\\Delta$ is locally finite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00615","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RSuO00jnsrR8pNLv4sORukSBa8qHvJgRnE+tXXmBNQXdnmr/7n1zqnM0VR+/lyBJQ2GlgUKoSLmGCQx9jyLfCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:53:29.996762Z"},"content_sha256":"25e261175cb092722aedcabd8555285fdc729a10ce80f99363a1640b666ed3bc","schema_version":"1.0","event_id":"sha256:25e261175cb092722aedcabd8555285fdc729a10ce80f99363a1640b666ed3bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SDYDSWGN3LVLXGIXE32CIIEC5Y/bundle.json","state_url":"https://pith.science/pith/SDYDSWGN3LVLXGIXE32CIIEC5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SDYDSWGN3LVLXGIXE32CIIEC5Y/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T18:53:29Z","links":{"resolver":"https://pith.science/pith/SDYDSWGN3LVLXGIXE32CIIEC5Y","bundle":"https://pith.science/pith/SDYDSWGN3LVLXGIXE32CIIEC5Y/bundle.json","state":"https://pith.science/pith/SDYDSWGN3LVLXGIXE32CIIEC5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SDYDSWGN3LVLXGIXE32CIIEC5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SDYDSWGN3LVLXGIXE32CIIEC5Y","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":"c26cd9dbd0438ef27116a96616382a97e8ecd92a0c205416fb781549b7e25e18","cross_cats_sorted":["math.DG","math.DS","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-03T16:15:11Z","title_canon_sha256":"afc08325403a2d61397e96e2eabfb140a9f8ca81b5afe7320936822058c761e3"},"schema_version":"1.0","source":{"id":"1610.00615","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00615","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00615v1","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00615","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"SDYDSWGN3LVL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SDYDSWGN3LVLXGIX","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SDYDSWGN","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:25e261175cb092722aedcabd8555285fdc729a10ce80f99363a1640b666ed3bc","target":"graph","created_at":"2026-05-18T00:32:36Z","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 $X$ be an $(n+1)$-dimensional manifold, $\\Delta$ be a one-dimensional foliation on $X$, and $p: X \\to X / \\Delta$ be a quotient map. We will say that a leaf $\\omega$ of $\\Delta$ is special whenever the space of leaves $X / \\Delta$ is not Hausdorff at $\\omega$. We present necessary and sufficient conditions for the map $p: X \\to X / \\Delta$ to be a locally trivial fibration under assumptions that all leaves of $\\Delta$ are non-compact and the family of all special leaves of $\\Delta$ is locally finite.","authors_text":"Eugene Polulyakh, Sergiy Maksymenko","cross_cats":["math.DG","math.DS","math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-03T16:15:11Z","title":"One-dimensional foliations on topological manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00615","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":"sha256:90a2326dcf0a7f6097e1d582351ac176c6cb69e885c05ca81707e00613ddb209","target":"record","created_at":"2026-05-18T00:32:36Z","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":"c26cd9dbd0438ef27116a96616382a97e8ecd92a0c205416fb781549b7e25e18","cross_cats_sorted":["math.DG","math.DS","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-03T16:15:11Z","title_canon_sha256":"afc08325403a2d61397e96e2eabfb140a9f8ca81b5afe7320936822058c761e3"},"schema_version":"1.0","source":{"id":"1610.00615","kind":"arxiv","version":1}},"canonical_sha256":"90f03958cddaeabb991726f4242082ee053a27a4152fd1bae570289f8e87aedd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90f03958cddaeabb991726f4242082ee053a27a4152fd1bae570289f8e87aedd","first_computed_at":"2026-05-18T00:32:36.413830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:36.413830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oSHykbHkBWkdDkpsFLxyS9z3AcI/k+UMrGRixd7VNGiSgTIKDzSRulnC0nzvAvDdIVXX8pCrImWcVoHw81fPAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:36.414461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00615","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90a2326dcf0a7f6097e1d582351ac176c6cb69e885c05ca81707e00613ddb209","sha256:25e261175cb092722aedcabd8555285fdc729a10ce80f99363a1640b666ed3bc"],"state_sha256":"db6bde8c4568fba74d8e03aed55c84fbe0d04019850d94d9c364f08c93afa112"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pE/cnKP9YIzKXACVytkXBMW/CE8PKORcI5VzJ/W5BSQI0kW8vBhGy/iErfvVkrSd3HSCzzJ/U2GAQI9TNDniCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:53:29.998692Z","bundle_sha256":"9f3afeb7c459497baf4820b6a2ef3d8a797824adaac94268865fc241a2e78e31"}}