{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OSD4UQIRRXA2RGDKOIZW7PRASB","short_pith_number":"pith:OSD4UQIR","canonical_record":{"source":{"id":"1012.2946","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-12-14T06:23:48Z","cross_cats_sorted":[],"title_canon_sha256":"791a550e894743c2196b20f0172630bfba3a7b36cae8be849c73825c29ab5e3d","abstract_canon_sha256":"1f8b0fecab5ebe7ddc2925f18288d72aa3f9d735f0ce39463ce6548f71e9fd4d"},"schema_version":"1.0"},"canonical_sha256":"7487ca41118dc1a8986a72336fbe209056868c005e49cedb7c54deec7c38060c","source":{"kind":"arxiv","id":"1012.2946","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2946","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2946v2","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2946","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"OSD4UQIRRXA2","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OSD4UQIRRXA2RGDK","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OSD4UQIR","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OSD4UQIRRXA2RGDKOIZW7PRASB","target":"record","payload":{"canonical_record":{"source":{"id":"1012.2946","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-12-14T06:23:48Z","cross_cats_sorted":[],"title_canon_sha256":"791a550e894743c2196b20f0172630bfba3a7b36cae8be849c73825c29ab5e3d","abstract_canon_sha256":"1f8b0fecab5ebe7ddc2925f18288d72aa3f9d735f0ce39463ce6548f71e9fd4d"},"schema_version":"1.0"},"canonical_sha256":"7487ca41118dc1a8986a72336fbe209056868c005e49cedb7c54deec7c38060c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:38.125530Z","signature_b64":"nHmsOxQt6BWq3lQsPQUb04V2aKWYKgVN3x6dSUrbKVBqGoy+dqheMno136V6pKvLoJ2PbVv05MRx0BTsB1YEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7487ca41118dc1a8986a72336fbe209056868c005e49cedb7c54deec7c38060c","last_reissued_at":"2026-05-18T03:33:38.124765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:38.124765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.2946","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sA3snaietWepOMb3VFWd5T7Bkl95+mpPiWqGwL1CMBqx5Wtk2ft0piwPD2Hc6/VPsl0ZaYW6ObfRACIIPOe/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:22:58.836997Z"},"content_sha256":"cfd542a10825adec83c3bc109352a67953cc2e48e8b793fcc749ed9800c108a5","schema_version":"1.0","event_id":"sha256:cfd542a10825adec83c3bc109352a67953cc2e48e8b793fcc749ed9800c108a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OSD4UQIRRXA2RGDKOIZW7PRASB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformation of locally free actions and the leafwise cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Masayuki Asaoka","submitted_at":"2010-12-14T06:23:48Z","abstract_excerpt":"This is a note of the author's lectures at \"Advanced courses in Foliation\" in the research program \"Foliation\", which was held at the Centre de Recerca Mathematica in the May of 2010. In this note, we discuss about the relationship between deformation of actions of Lie groups and the leafwise cohomology of the orbit foliation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2946","kind":"arxiv","version":2},"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":"2026-05-18T03:33:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EkJwUnuxRcpvUfLsRqqkp0ApCMBvmFMHgZVoo0zkusGlBcPmoyG7JVVlfkZfbf0xXpa8cwMOhUNUh2CLx+aLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:22:58.837365Z"},"content_sha256":"2e348d52feb5270acc6b678a4580dd3af5cfdd4228439f5471c16b4dab942da1","schema_version":"1.0","event_id":"sha256:2e348d52feb5270acc6b678a4580dd3af5cfdd4228439f5471c16b4dab942da1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OSD4UQIRRXA2RGDKOIZW7PRASB/bundle.json","state_url":"https://pith.science/pith/OSD4UQIRRXA2RGDKOIZW7PRASB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OSD4UQIRRXA2RGDKOIZW7PRASB/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":"2026-06-01T09:22:58Z","links":{"resolver":"https://pith.science/pith/OSD4UQIRRXA2RGDKOIZW7PRASB","bundle":"https://pith.science/pith/OSD4UQIRRXA2RGDKOIZW7PRASB/bundle.json","state":"https://pith.science/pith/OSD4UQIRRXA2RGDKOIZW7PRASB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OSD4UQIRRXA2RGDKOIZW7PRASB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OSD4UQIRRXA2RGDKOIZW7PRASB","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":"1f8b0fecab5ebe7ddc2925f18288d72aa3f9d735f0ce39463ce6548f71e9fd4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-12-14T06:23:48Z","title_canon_sha256":"791a550e894743c2196b20f0172630bfba3a7b36cae8be849c73825c29ab5e3d"},"schema_version":"1.0","source":{"id":"1012.2946","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2946","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2946v2","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2946","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"OSD4UQIRRXA2","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OSD4UQIRRXA2RGDK","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OSD4UQIR","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:2e348d52feb5270acc6b678a4580dd3af5cfdd4228439f5471c16b4dab942da1","target":"graph","created_at":"2026-05-18T03:33:38Z","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":"This is a note of the author's lectures at \"Advanced courses in Foliation\" in the research program \"Foliation\", which was held at the Centre de Recerca Mathematica in the May of 2010. In this note, we discuss about the relationship between deformation of actions of Lie groups and the leafwise cohomology of the orbit foliation.","authors_text":"Masayuki Asaoka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-12-14T06:23:48Z","title":"Deformation of locally free actions and the leafwise cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2946","kind":"arxiv","version":2},"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:cfd542a10825adec83c3bc109352a67953cc2e48e8b793fcc749ed9800c108a5","target":"record","created_at":"2026-05-18T03:33:38Z","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":"1f8b0fecab5ebe7ddc2925f18288d72aa3f9d735f0ce39463ce6548f71e9fd4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-12-14T06:23:48Z","title_canon_sha256":"791a550e894743c2196b20f0172630bfba3a7b36cae8be849c73825c29ab5e3d"},"schema_version":"1.0","source":{"id":"1012.2946","kind":"arxiv","version":2}},"canonical_sha256":"7487ca41118dc1a8986a72336fbe209056868c005e49cedb7c54deec7c38060c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7487ca41118dc1a8986a72336fbe209056868c005e49cedb7c54deec7c38060c","first_computed_at":"2026-05-18T03:33:38.124765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:38.124765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nHmsOxQt6BWq3lQsPQUb04V2aKWYKgVN3x6dSUrbKVBqGoy+dqheMno136V6pKvLoJ2PbVv05MRx0BTsB1YEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:38.125530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2946","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfd542a10825adec83c3bc109352a67953cc2e48e8b793fcc749ed9800c108a5","sha256:2e348d52feb5270acc6b678a4580dd3af5cfdd4228439f5471c16b4dab942da1"],"state_sha256":"1fec976aa032f31a265efc8759b70aa6d18f715ca1f0722863d39d02746663d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l4B3X1QM4anjtliwKtO6J9GgfDeeWyewWjnsyqQp1Y/Nzad3Ylmt6lz7dbH1gNKHCqgKOUG4S/J+/3MSuFuqDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:22:58.839300Z","bundle_sha256":"3cce8640c610b8985042a4bf5b365c9759f146a70dd27f2eafdf2b5234297310"}}