{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:SPYLDKYVMMN6ZSWQBY5MI2HHE6","short_pith_number":"pith:SPYLDKYV","canonical_record":{"source":{"id":"math/9808064","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"1998-08-14T21:19:47Z","cross_cats_sorted":[],"title_canon_sha256":"3912d3b7f8dbd9943cd291b686816d53aa8f274bd8128808278d631fec52a0ff","abstract_canon_sha256":"78b6224a630fb634eae8f0bfc58479b81d35354fc73ef05a6f1ac69de51d95f5"},"schema_version":"1.0"},"canonical_sha256":"93f0b1ab15631beccad00e3ac468e72794c2b2ec5ffabcb3ac3ecf976088a361","source":{"kind":"arxiv","id":"math/9808064","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9808064","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/9808064v3","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9808064","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"SPYLDKYVMMN6","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"SPYLDKYVMMN6ZSWQ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"SPYLDKYV","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:SPYLDKYVMMN6ZSWQBY5MI2HHE6","target":"record","payload":{"canonical_record":{"source":{"id":"math/9808064","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"1998-08-14T21:19:47Z","cross_cats_sorted":[],"title_canon_sha256":"3912d3b7f8dbd9943cd291b686816d53aa8f274bd8128808278d631fec52a0ff","abstract_canon_sha256":"78b6224a630fb634eae8f0bfc58479b81d35354fc73ef05a6f1ac69de51d95f5"},"schema_version":"1.0"},"canonical_sha256":"93f0b1ab15631beccad00e3ac468e72794c2b2ec5ffabcb3ac3ecf976088a361","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:59.297242Z","signature_b64":"FQKLSrZ5awtmu/4x9QpBZ4C2HetSyuw2CHwqif/W4Y90Ak3TjUVTfh+3c++qAHoPyWMl63CyXZIeAlKdfZwWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93f0b1ab15631beccad00e3ac468e72794c2b2ec5ffabcb3ac3ecf976088a361","last_reissued_at":"2026-05-18T02:37:59.296910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:59.296910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9808064","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0nGWBs08LhUaR0xCnpbd8TEA580MApGr70AADbBHB3/yeU79uaN/fLUAfMhg0dJDHvBcWdPiaD6vCfaKAzznCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:57:52.296271Z"},"content_sha256":"0b51e8d299bdf18c95070a7605fcb2dc3b927ae6b5bf24ba763b068a844505aa","schema_version":"1.0","event_id":"sha256:0b51e8d299bdf18c95070a7605fcb2dc3b927ae6b5bf24ba763b068a844505aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:SPYLDKYVMMN6ZSWQBY5MI2HHE6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"R-covered foliations of hyperbolic 3-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Danny Calegari","submitted_at":"1998-08-14T21:19:47Z","abstract_excerpt":"We produce examples of taut foliations of hyperbolic 3-manifolds which are R-covered but not uniform --- ie the leaf space of the universal cover is R, but pairs of leaves are not contained in bounded neighborhoods of each other. This answers in the negative a conjecture of Thurston `Three-manifolds, foliations and circles I' (math.GT/9712268). We further show that these foliations can be chosen to be C^0 close to foliations by closed surfaces. Our construction underscores the importance of the existence of transverse regulating vector fields and cone fields for R-covered foliations. Finally, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9808064","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2/Y55Aqv4f+8pJlQfBVA1LZauITkDBatUB3mtP0r7VfZQYjUr256+/IR92oKlAvCeIUWkR3ghOupgfpz8xUhDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:57:52.296674Z"},"content_sha256":"ad06ccb02d390d5da1596d63b33733df15236182f73dbfbb013d03c8e9c1b2f0","schema_version":"1.0","event_id":"sha256:ad06ccb02d390d5da1596d63b33733df15236182f73dbfbb013d03c8e9c1b2f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SPYLDKYVMMN6ZSWQBY5MI2HHE6/bundle.json","state_url":"https://pith.science/pith/SPYLDKYVMMN6ZSWQBY5MI2HHE6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SPYLDKYVMMN6ZSWQBY5MI2HHE6/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":"2026-05-28T21:57:52Z","links":{"resolver":"https://pith.science/pith/SPYLDKYVMMN6ZSWQBY5MI2HHE6","bundle":"https://pith.science/pith/SPYLDKYVMMN6ZSWQBY5MI2HHE6/bundle.json","state":"https://pith.science/pith/SPYLDKYVMMN6ZSWQBY5MI2HHE6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SPYLDKYVMMN6ZSWQBY5MI2HHE6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:SPYLDKYVMMN6ZSWQBY5MI2HHE6","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":"78b6224a630fb634eae8f0bfc58479b81d35354fc73ef05a6f1ac69de51d95f5","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"1998-08-14T21:19:47Z","title_canon_sha256":"3912d3b7f8dbd9943cd291b686816d53aa8f274bd8128808278d631fec52a0ff"},"schema_version":"1.0","source":{"id":"math/9808064","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9808064","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/9808064v3","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9808064","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"SPYLDKYVMMN6","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"SPYLDKYVMMN6ZSWQ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"SPYLDKYV","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:ad06ccb02d390d5da1596d63b33733df15236182f73dbfbb013d03c8e9c1b2f0","target":"graph","created_at":"2026-05-18T02:37:59Z","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":"We produce examples of taut foliations of hyperbolic 3-manifolds which are R-covered but not uniform --- ie the leaf space of the universal cover is R, but pairs of leaves are not contained in bounded neighborhoods of each other. This answers in the negative a conjecture of Thurston `Three-manifolds, foliations and circles I' (math.GT/9712268). We further show that these foliations can be chosen to be C^0 close to foliations by closed surfaces. Our construction underscores the importance of the existence of transverse regulating vector fields and cone fields for R-covered foliations. Finally, ","authors_text":"Danny Calegari","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"1998-08-14T21:19:47Z","title":"R-covered foliations of hyperbolic 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9808064","kind":"arxiv","version":3},"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":"sha256:0b51e8d299bdf18c95070a7605fcb2dc3b927ae6b5bf24ba763b068a844505aa","target":"record","created_at":"2026-05-18T02:37:59Z","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":"78b6224a630fb634eae8f0bfc58479b81d35354fc73ef05a6f1ac69de51d95f5","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"1998-08-14T21:19:47Z","title_canon_sha256":"3912d3b7f8dbd9943cd291b686816d53aa8f274bd8128808278d631fec52a0ff"},"schema_version":"1.0","source":{"id":"math/9808064","kind":"arxiv","version":3}},"canonical_sha256":"93f0b1ab15631beccad00e3ac468e72794c2b2ec5ffabcb3ac3ecf976088a361","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93f0b1ab15631beccad00e3ac468e72794c2b2ec5ffabcb3ac3ecf976088a361","first_computed_at":"2026-05-18T02:37:59.296910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:59.296910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FQKLSrZ5awtmu/4x9QpBZ4C2HetSyuw2CHwqif/W4Y90Ak3TjUVTfh+3c++qAHoPyWMl63CyXZIeAlKdfZwWDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:59.297242Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9808064","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b51e8d299bdf18c95070a7605fcb2dc3b927ae6b5bf24ba763b068a844505aa","sha256:ad06ccb02d390d5da1596d63b33733df15236182f73dbfbb013d03c8e9c1b2f0"],"state_sha256":"b553921f9ec543a13d0f08ae663c77c19b89c36117e95456712ff15a40f5e4ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ZdIb3aQ/EFZJIIchKq3BbQQgdFh/mEqxIbN7IUH//nFpR3lOQVwFzA44OR2dzZFhOrpov9BwF18oZxW/tnPDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:57:52.299232Z","bundle_sha256":"0ed99347a4e3c789bdb993a8e660e89277583b7d1dd0de158e428df8e423a61c"}}