{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RXSAJLA7SHL7RXKBMPSTSD3ODK","short_pith_number":"pith:RXSAJLA7","canonical_record":{"source":{"id":"1511.05830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-18T15:20:30Z","cross_cats_sorted":[],"title_canon_sha256":"9f2c1185b242ef4279e428f01bd98ae13990776b2d092ef1a1029ad2f509231a","abstract_canon_sha256":"c6fcecc60f0be2511922dd09135891312cdd9e0ae4c7f73f3597256e4b746b1a"},"schema_version":"1.0"},"canonical_sha256":"8de404ac1f91d7f8dd4163e5390f6e1aa93c99069d4bdde6d7c4640cb1ab4afe","source":{"kind":"arxiv","id":"1511.05830","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05830","created_at":"2026-05-18T01:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05830v1","created_at":"2026-05-18T01:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05830","created_at":"2026-05-18T01:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"RXSAJLA7SHL7","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RXSAJLA7SHL7RXKB","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RXSAJLA7","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RXSAJLA7SHL7RXKBMPSTSD3ODK","target":"record","payload":{"canonical_record":{"source":{"id":"1511.05830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-18T15:20:30Z","cross_cats_sorted":[],"title_canon_sha256":"9f2c1185b242ef4279e428f01bd98ae13990776b2d092ef1a1029ad2f509231a","abstract_canon_sha256":"c6fcecc60f0be2511922dd09135891312cdd9e0ae4c7f73f3597256e4b746b1a"},"schema_version":"1.0"},"canonical_sha256":"8de404ac1f91d7f8dd4163e5390f6e1aa93c99069d4bdde6d7c4640cb1ab4afe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:32.511675Z","signature_b64":"rd9iXpg69L3DyzcuvHxklqL/Egn5dRXi0CgVnlE6Y388UfF3wQv8qcmWwlrT+XrJlBuCEdwjR76fqk8s0vw1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8de404ac1f91d7f8dd4163e5390f6e1aa93c99069d4bdde6d7c4640cb1ab4afe","last_reissued_at":"2026-05-18T01:26:32.510974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:32.510974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.05830","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":"2026-05-18T01:26:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jY083DCiubAh2tsJjcV4H6ox7V6v5Pw/WrGQjStEDhCydKO2fEYMZWDq5PiILOYFEYUEcoZxmUVz2ghck1BRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:34:50.639121Z"},"content_sha256":"9581d4b5bd2a86e7b647a0df90c31b88ce1bc6f771d97b5c3866ac027ed2bc32","schema_version":"1.0","event_id":"sha256:9581d4b5bd2a86e7b647a0df90c31b88ce1bc6f771d97b5c3866ac027ed2bc32"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RXSAJLA7SHL7RXKBMPSTSD3ODK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Horizontal holonomy and foliated manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"E. Grong, F. Jean, P. Kokkonen, Y. Chitour","submitted_at":"2015-11-18T15:20:30Z","abstract_excerpt":"We introduce horizontal holonomy groups, which are groups defined using parallel transport only along curves tangent to a given subbundle $D$ of the tangent bundle. We provide explicit means of computing these holonomy groups by deriving analogues of Ambrose-Singer's and Ozeki's theorems. We then give necessary and sufficient conditions in terms of the horizontal holonomy groups for existence of solutions of two problems on foliated manifolds: determining when a foliation can be either (a) totally geodesic or (b) endowed with a principal bundle structure. The subbundle $D$ plays the role of an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05830","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":"2026-05-18T01:26:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Eu6vxNEAP9YpxW3YVRGUWk7+X3ZJyRxpsWHkd/u0BeCsVdK+dx8R6b0e61VuvIpaEZ4NPvtfJvJJoYZEnwtCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:34:50.639481Z"},"content_sha256":"d3de8b211b873e406e222df57ca137c9fc97a0a6d2510ccdba965ddc3c0209e8","schema_version":"1.0","event_id":"sha256:d3de8b211b873e406e222df57ca137c9fc97a0a6d2510ccdba965ddc3c0209e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RXSAJLA7SHL7RXKBMPSTSD3ODK/bundle.json","state_url":"https://pith.science/pith/RXSAJLA7SHL7RXKBMPSTSD3ODK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RXSAJLA7SHL7RXKBMPSTSD3ODK/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":"2026-06-03T08:34:50Z","links":{"resolver":"https://pith.science/pith/RXSAJLA7SHL7RXKBMPSTSD3ODK","bundle":"https://pith.science/pith/RXSAJLA7SHL7RXKBMPSTSD3ODK/bundle.json","state":"https://pith.science/pith/RXSAJLA7SHL7RXKBMPSTSD3ODK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RXSAJLA7SHL7RXKBMPSTSD3ODK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RXSAJLA7SHL7RXKBMPSTSD3ODK","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":"c6fcecc60f0be2511922dd09135891312cdd9e0ae4c7f73f3597256e4b746b1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-18T15:20:30Z","title_canon_sha256":"9f2c1185b242ef4279e428f01bd98ae13990776b2d092ef1a1029ad2f509231a"},"schema_version":"1.0","source":{"id":"1511.05830","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05830","created_at":"2026-05-18T01:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05830v1","created_at":"2026-05-18T01:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05830","created_at":"2026-05-18T01:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"RXSAJLA7SHL7","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RXSAJLA7SHL7RXKB","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RXSAJLA7","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:d3de8b211b873e406e222df57ca137c9fc97a0a6d2510ccdba965ddc3c0209e8","target":"graph","created_at":"2026-05-18T01:26:32Z","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 introduce horizontal holonomy groups, which are groups defined using parallel transport only along curves tangent to a given subbundle $D$ of the tangent bundle. We provide explicit means of computing these holonomy groups by deriving analogues of Ambrose-Singer's and Ozeki's theorems. We then give necessary and sufficient conditions in terms of the horizontal holonomy groups for existence of solutions of two problems on foliated manifolds: determining when a foliation can be either (a) totally geodesic or (b) endowed with a principal bundle structure. The subbundle $D$ plays the role of an","authors_text":"E. Grong, F. Jean, P. Kokkonen, Y. Chitour","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-18T15:20:30Z","title":"Horizontal holonomy and foliated manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05830","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":"sha256:9581d4b5bd2a86e7b647a0df90c31b88ce1bc6f771d97b5c3866ac027ed2bc32","target":"record","created_at":"2026-05-18T01:26:32Z","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":"c6fcecc60f0be2511922dd09135891312cdd9e0ae4c7f73f3597256e4b746b1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-18T15:20:30Z","title_canon_sha256":"9f2c1185b242ef4279e428f01bd98ae13990776b2d092ef1a1029ad2f509231a"},"schema_version":"1.0","source":{"id":"1511.05830","kind":"arxiv","version":1}},"canonical_sha256":"8de404ac1f91d7f8dd4163e5390f6e1aa93c99069d4bdde6d7c4640cb1ab4afe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8de404ac1f91d7f8dd4163e5390f6e1aa93c99069d4bdde6d7c4640cb1ab4afe","first_computed_at":"2026-05-18T01:26:32.510974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:32.510974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rd9iXpg69L3DyzcuvHxklqL/Egn5dRXi0CgVnlE6Y388UfF3wQv8qcmWwlrT+XrJlBuCEdwjR76fqk8s0vw1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:32.511675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05830","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9581d4b5bd2a86e7b647a0df90c31b88ce1bc6f771d97b5c3866ac027ed2bc32","sha256:d3de8b211b873e406e222df57ca137c9fc97a0a6d2510ccdba965ddc3c0209e8"],"state_sha256":"a14e5bbfa605499d274bc34587e2d4992562bad0ba15b45cb83207c2590225ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCDkxPGz/tsJIKajj45e3WLSwjbZYb/lE/Gi9WWun7ICdb7L163zd7+FBLBrzYkv7are6D95JPwJJyjuV7Q9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:34:50.641339Z","bundle_sha256":"c70b8e88370656811ef99b5cd3f2e4d499731e684675a6c881d0e69ac92c512b"}}