{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QJ6CUKASPLUNXSWUNIVN7FWW6C","short_pith_number":"pith:QJ6CUKAS","canonical_record":{"source":{"id":"1203.6829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-30T14:31:57Z","cross_cats_sorted":[],"title_canon_sha256":"3a35f0554f78782ae4c802494dd529a54e8a29fd5847b08010f2a7978097ac7f","abstract_canon_sha256":"d6e24e6aa986599dd063765c76ce72db706f1896e5fdc86a15dfcd8ef08f2fbb"},"schema_version":"1.0"},"canonical_sha256":"827c2a28127ae8dbcad46a2adf96d6f0a8ae94731afd883affcf790ce8700caf","source":{"kind":"arxiv","id":"1203.6829","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6829","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6829v1","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6829","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"QJ6CUKASPLUN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QJ6CUKASPLUNXSWU","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QJ6CUKAS","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QJ6CUKASPLUNXSWUNIVN7FWW6C","target":"record","payload":{"canonical_record":{"source":{"id":"1203.6829","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-30T14:31:57Z","cross_cats_sorted":[],"title_canon_sha256":"3a35f0554f78782ae4c802494dd529a54e8a29fd5847b08010f2a7978097ac7f","abstract_canon_sha256":"d6e24e6aa986599dd063765c76ce72db706f1896e5fdc86a15dfcd8ef08f2fbb"},"schema_version":"1.0"},"canonical_sha256":"827c2a28127ae8dbcad46a2adf96d6f0a8ae94731afd883affcf790ce8700caf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:06.226282Z","signature_b64":"TGajGimIuWz8QdwngDm0OiKDComfgT+H0kA4f6EfTN0flAOWI04onID3m/p0MiY2JqhYRZAoreXlqKs2GtgpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"827c2a28127ae8dbcad46a2adf96d6f0a8ae94731afd883affcf790ce8700caf","last_reissued_at":"2026-05-18T03:22:06.225584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:06.225584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.6829","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":"2026-05-18T03:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fiYQd5CLStF6leHHdijRchVcM8MnIu9SL1RQRmOfaVijDg06Tu/6uV6V+yMosoDvFTnsHohsKa8VI46ZDWsXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:08:30.983584Z"},"content_sha256":"a04c98a1cbe4a9c0a7d7442c537ff0410041d4a1ffcc0a7d72ba8498f55671a6","schema_version":"1.0","event_id":"sha256:a04c98a1cbe4a9c0a7d7442c537ff0410041d4a1ffcc0a7d72ba8498f55671a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QJ6CUKASPLUNXSWUNIVN7FWW6C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Progress in the Theory of Singular Riemannian Foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dirk Toeben, Marcos M. Alexandrino, Rafael Briquet","submitted_at":"2012-03-30T14:31:57Z","abstract_excerpt":"A singular foliation is called a singular Riemannian foliation (SRF) if every geodesic that is perpendicular to one leaf is perpendicular to every leaf it meets. A typical example is the partition of a complete Riemannian manifold into orbits of an isometric action.\n  In this survey, we provide an introduction to the theory of SRFs, leading from the foundations to recent developments in research on this subject. Sketches of proofs are included and useful techniques are emphasized. We study the local structure of SRFs in general and under curvature conditions. We review the solution of the Pala"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6829","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":"2026-05-18T03:22:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kyoC70uG/+l4rw0HGlvyR1dxrnuHJgxKVpitUKvUzXPbkvpp4Sw9RGvpg5H6VuQ0lOdkXeBzRJe16dE6g4G0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:08:30.983951Z"},"content_sha256":"c2ebf6b6df6c03a1c62614bde3950f3cc1b5ef49a873d50ebc4af82bbcbae379","schema_version":"1.0","event_id":"sha256:c2ebf6b6df6c03a1c62614bde3950f3cc1b5ef49a873d50ebc4af82bbcbae379"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJ6CUKASPLUNXSWUNIVN7FWW6C/bundle.json","state_url":"https://pith.science/pith/QJ6CUKASPLUNXSWUNIVN7FWW6C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJ6CUKASPLUNXSWUNIVN7FWW6C/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":"2026-06-03T15:08:30Z","links":{"resolver":"https://pith.science/pith/QJ6CUKASPLUNXSWUNIVN7FWW6C","bundle":"https://pith.science/pith/QJ6CUKASPLUNXSWUNIVN7FWW6C/bundle.json","state":"https://pith.science/pith/QJ6CUKASPLUNXSWUNIVN7FWW6C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJ6CUKASPLUNXSWUNIVN7FWW6C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QJ6CUKASPLUNXSWUNIVN7FWW6C","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":"d6e24e6aa986599dd063765c76ce72db706f1896e5fdc86a15dfcd8ef08f2fbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-30T14:31:57Z","title_canon_sha256":"3a35f0554f78782ae4c802494dd529a54e8a29fd5847b08010f2a7978097ac7f"},"schema_version":"1.0","source":{"id":"1203.6829","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6829","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6829v1","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6829","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"QJ6CUKASPLUN","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QJ6CUKASPLUNXSWU","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QJ6CUKAS","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:c2ebf6b6df6c03a1c62614bde3950f3cc1b5ef49a873d50ebc4af82bbcbae379","target":"graph","created_at":"2026-05-18T03:22:06Z","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":"A singular foliation is called a singular Riemannian foliation (SRF) if every geodesic that is perpendicular to one leaf is perpendicular to every leaf it meets. A typical example is the partition of a complete Riemannian manifold into orbits of an isometric action.\n  In this survey, we provide an introduction to the theory of SRFs, leading from the foundations to recent developments in research on this subject. Sketches of proofs are included and useful techniques are emphasized. We study the local structure of SRFs in general and under curvature conditions. We review the solution of the Pala","authors_text":"Dirk Toeben, Marcos M. Alexandrino, Rafael Briquet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-30T14:31:57Z","title":"Progress in the Theory of Singular Riemannian Foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6829","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:a04c98a1cbe4a9c0a7d7442c537ff0410041d4a1ffcc0a7d72ba8498f55671a6","target":"record","created_at":"2026-05-18T03:22:06Z","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":"d6e24e6aa986599dd063765c76ce72db706f1896e5fdc86a15dfcd8ef08f2fbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-30T14:31:57Z","title_canon_sha256":"3a35f0554f78782ae4c802494dd529a54e8a29fd5847b08010f2a7978097ac7f"},"schema_version":"1.0","source":{"id":"1203.6829","kind":"arxiv","version":1}},"canonical_sha256":"827c2a28127ae8dbcad46a2adf96d6f0a8ae94731afd883affcf790ce8700caf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"827c2a28127ae8dbcad46a2adf96d6f0a8ae94731afd883affcf790ce8700caf","first_computed_at":"2026-05-18T03:22:06.225584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:06.225584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TGajGimIuWz8QdwngDm0OiKDComfgT+H0kA4f6EfTN0flAOWI04onID3m/p0MiY2JqhYRZAoreXlqKs2GtgpDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:06.226282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6829","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a04c98a1cbe4a9c0a7d7442c537ff0410041d4a1ffcc0a7d72ba8498f55671a6","sha256:c2ebf6b6df6c03a1c62614bde3950f3cc1b5ef49a873d50ebc4af82bbcbae379"],"state_sha256":"19d276e49ba7491523bf0371aea707e95d3020c47b0a0a4c3b7de089e4ecedc1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1s7tkBgrIp3ulI94r+Wg0Jn8TBUOuhSDtAPQonUJbjjYzY7gxLgqPIto/zFDTBi7CTAeEdXLh8ARjRI71dWMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:08:30.985918Z","bundle_sha256":"3f0fbe1f967c2793e57601e268561d880e2a1725022f2977fd8c45f466730869"}}