{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SGJ5WBZKYDVQQJQ5T676VKSPCA","short_pith_number":"pith:SGJ5WBZK","canonical_record":{"source":{"id":"1108.2765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-13T06:47:48Z","cross_cats_sorted":[],"title_canon_sha256":"3566688d62262aa12e4af31dcd16ad83d04159c3bb7340e1e3c04f77dd97e0ad","abstract_canon_sha256":"342568579f85547ca77613549aeafed2742a378d4b6cf724d68550392858bf52"},"schema_version":"1.0"},"canonical_sha256":"9193db072ac0eb08261d9fbfeaaa4f101db8b3724c1610c89e0967413961fe4d","source":{"kind":"arxiv","id":"1108.2765","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2765","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2765v1","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2765","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"pith_short_12","alias_value":"SGJ5WBZKYDVQ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SGJ5WBZKYDVQQJQ5","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SGJ5WBZK","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SGJ5WBZKYDVQQJQ5T676VKSPCA","target":"record","payload":{"canonical_record":{"source":{"id":"1108.2765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-13T06:47:48Z","cross_cats_sorted":[],"title_canon_sha256":"3566688d62262aa12e4af31dcd16ad83d04159c3bb7340e1e3c04f77dd97e0ad","abstract_canon_sha256":"342568579f85547ca77613549aeafed2742a378d4b6cf724d68550392858bf52"},"schema_version":"1.0"},"canonical_sha256":"9193db072ac0eb08261d9fbfeaaa4f101db8b3724c1610c89e0967413961fe4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:05.353913Z","signature_b64":"hrh2dsibTyPgboszqRff87TmuWRdbkJBeEVSlCcXrgTFcn0dECTrP+aGvjJDDnWdbga6BdKjWdmZJjCgQd2uCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9193db072ac0eb08261d9fbfeaaa4f101db8b3724c1610c89e0967413961fe4d","last_reissued_at":"2026-05-18T03:43:05.353380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:05.353380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.2765","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":"2026-05-18T03:43:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPZdHE/OeN/N6AnSfR8cGF6UlA/2L/9WHK+JZ50v44VIr1Khf8R34MFAQZGp8v7AoJpRYkp0q0pwNX1yRRbFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:18:54.602721Z"},"content_sha256":"dcaae845b63ad778e94982be305cffa74935d8fcca677fd199db9935880f8099","schema_version":"1.0","event_id":"sha256:dcaae845b63ad778e94982be305cffa74935d8fcca677fd199db9935880f8099"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SGJ5WBZKYDVQQJQ5T676VKSPCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Haefliger's codimension-one singular foliations, open books and twisted open books in dimension 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Francois Laudenbach (LMJL), Gael Gael Meigniez (LMAM)","submitted_at":"2011-08-13T06:47:48Z","abstract_excerpt":"We consider singular foliations of codimension one on 3-manifolds, in the sense defined by A. Haefliger as being Gamma_1-structures. We prove that under the obvious linear embedding condition, they are Gamma_1-homotopic to a regular foliation carried by an open book or a twisted open book. The latter concept is introduced for this aim. Our result holds true in every regularity C^r, r at least 1. In particular, in dimension 3, this gives a very simple proof of Thurston's 1976 regularization theorem without using Mather's homology equivalence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2765","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":"2026-05-18T03:43:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mAHqd5vi7fkbobroRlXvk5Pjt72fW7MeebRJ+dUTHTcXyO5YkOy//fmxOTDT1ZWaLngRn6cHZkbxJgnOa7+bBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:18:54.603067Z"},"content_sha256":"5932cec9b4849ec6a18f27d78f4f9632efd035464bb9c7572e01f0a1c1aae594","schema_version":"1.0","event_id":"sha256:5932cec9b4849ec6a18f27d78f4f9632efd035464bb9c7572e01f0a1c1aae594"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SGJ5WBZKYDVQQJQ5T676VKSPCA/bundle.json","state_url":"https://pith.science/pith/SGJ5WBZKYDVQQJQ5T676VKSPCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SGJ5WBZKYDVQQJQ5T676VKSPCA/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":"2026-06-20T22:18:54Z","links":{"resolver":"https://pith.science/pith/SGJ5WBZKYDVQQJQ5T676VKSPCA","bundle":"https://pith.science/pith/SGJ5WBZKYDVQQJQ5T676VKSPCA/bundle.json","state":"https://pith.science/pith/SGJ5WBZKYDVQQJQ5T676VKSPCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SGJ5WBZKYDVQQJQ5T676VKSPCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SGJ5WBZKYDVQQJQ5T676VKSPCA","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":"342568579f85547ca77613549aeafed2742a378d4b6cf724d68550392858bf52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-13T06:47:48Z","title_canon_sha256":"3566688d62262aa12e4af31dcd16ad83d04159c3bb7340e1e3c04f77dd97e0ad"},"schema_version":"1.0","source":{"id":"1108.2765","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2765","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2765v1","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2765","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"pith_short_12","alias_value":"SGJ5WBZKYDVQ","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SGJ5WBZKYDVQQJQ5","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SGJ5WBZK","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:5932cec9b4849ec6a18f27d78f4f9632efd035464bb9c7572e01f0a1c1aae594","target":"graph","created_at":"2026-05-18T03:43:05Z","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 consider singular foliations of codimension one on 3-manifolds, in the sense defined by A. Haefliger as being Gamma_1-structures. We prove that under the obvious linear embedding condition, they are Gamma_1-homotopic to a regular foliation carried by an open book or a twisted open book. The latter concept is introduced for this aim. Our result holds true in every regularity C^r, r at least 1. In particular, in dimension 3, this gives a very simple proof of Thurston's 1976 regularization theorem without using Mather's homology equivalence.","authors_text":"Francois Laudenbach (LMJL), Gael Gael Meigniez (LMAM)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-13T06:47:48Z","title":"Haefliger's codimension-one singular foliations, open books and twisted open books in dimension 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2765","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:dcaae845b63ad778e94982be305cffa74935d8fcca677fd199db9935880f8099","target":"record","created_at":"2026-05-18T03:43:05Z","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":"342568579f85547ca77613549aeafed2742a378d4b6cf724d68550392858bf52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-13T06:47:48Z","title_canon_sha256":"3566688d62262aa12e4af31dcd16ad83d04159c3bb7340e1e3c04f77dd97e0ad"},"schema_version":"1.0","source":{"id":"1108.2765","kind":"arxiv","version":1}},"canonical_sha256":"9193db072ac0eb08261d9fbfeaaa4f101db8b3724c1610c89e0967413961fe4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9193db072ac0eb08261d9fbfeaaa4f101db8b3724c1610c89e0967413961fe4d","first_computed_at":"2026-05-18T03:43:05.353380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:05.353380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hrh2dsibTyPgboszqRff87TmuWRdbkJBeEVSlCcXrgTFcn0dECTrP+aGvjJDDnWdbga6BdKjWdmZJjCgQd2uCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:05.353913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2765","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcaae845b63ad778e94982be305cffa74935d8fcca677fd199db9935880f8099","sha256:5932cec9b4849ec6a18f27d78f4f9632efd035464bb9c7572e01f0a1c1aae594"],"state_sha256":"cdc778836b5a4d75fe255ad015ac43855585e3105bc0bc74cd89ff9093cfcf4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTqORnd9/LU8Gb6KWKAHM7h5J2QAjqrYdrHfSrWgMUE0YVuO6KTFrORbl/xgbNLM8jEP74WorfgpHnGjV8ffDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:18:54.605380Z","bundle_sha256":"5c47120575bdb1191cafe22299a367efeba349cafa930a424737e8a99c20f1c3"}}