{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OJE6YFYVA7LGL23RUERYDOYENW","short_pith_number":"pith:OJE6YFYV","canonical_record":{"source":{"id":"1203.6113","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-27T23:35:24Z","cross_cats_sorted":[],"title_canon_sha256":"68a19e9c389869d8acaae1045a39a64591a8ea73a2811fa23e130f12f441a48f","abstract_canon_sha256":"20d21fb5cfa0fc43102a3aff077fac14bbfc535f22c2debf21783c0b18a98006"},"schema_version":"1.0"},"canonical_sha256":"7249ec171507d665eb71a12381bb046db431f992a744a795e8ba67667ef6849d","source":{"kind":"arxiv","id":"1203.6113","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6113","created_at":"2026-05-18T03:59:04Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6113v1","created_at":"2026-05-18T03:59:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6113","created_at":"2026-05-18T03:59:04Z"},{"alias_kind":"pith_short_12","alias_value":"OJE6YFYVA7LG","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OJE6YFYVA7LGL23R","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OJE6YFYV","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OJE6YFYVA7LGL23RUERYDOYENW","target":"record","payload":{"canonical_record":{"source":{"id":"1203.6113","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-27T23:35:24Z","cross_cats_sorted":[],"title_canon_sha256":"68a19e9c389869d8acaae1045a39a64591a8ea73a2811fa23e130f12f441a48f","abstract_canon_sha256":"20d21fb5cfa0fc43102a3aff077fac14bbfc535f22c2debf21783c0b18a98006"},"schema_version":"1.0"},"canonical_sha256":"7249ec171507d665eb71a12381bb046db431f992a744a795e8ba67667ef6849d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:04.128278Z","signature_b64":"3Jz+W2LKBsYjMizVZDCKlJfrEqDnh4cRB0DU3reUA5LUFdLIXAdBAywFbbTsImr8m+0l72mG4gq8S26WqF5fCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7249ec171507d665eb71a12381bb046db431f992a744a795e8ba67667ef6849d","last_reissued_at":"2026-05-18T03:59:04.127442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:04.127442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.6113","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":"2026-05-18T03:59:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CKHfU3IbQR0q+WscmRvFFQBIaEA0leC4fNec0wurXlMujJX8mr54IcQJAUB5+7nmX1Wt9os+e8JUP6JZKo7pCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:03:50.462907Z"},"content_sha256":"0be66d02af59ff420c5e770eae74b9a8e2e6521962c9856e93fbf2ee95e8ad47","schema_version":"1.0","event_id":"sha256:0be66d02af59ff420c5e770eae74b9a8e2e6521962c9856e93fbf2ee95e8ad47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OJE6YFYVA7LGL23RUERYDOYENW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low dimensional Singular Riemannian Foliations in spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Marco Radeschi","submitted_at":"2012-03-27T23:35:24Z","abstract_excerpt":"Singular Riemannian Foliations are particular types of foliations on Riemannian manifolds, in which leaves locally stay at a constant distance from each other. Singular Riemannian Foliations in round spheres play a special role, since they provide \"infinitesimal information\" about general Singular Riemannian Foliations. In this paper we show that Singular Riemannian Foliations in spheres, of dimension at most 3, are orbits of an isometric group action."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6113","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":"2026-05-18T03:59:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8KCKO1speG5IdY9qgMPIdUymap91tk40ii/h0n4fQ9XN7KpQ+JOhVekWVYM3tBhTftaIhxyFH28L/8JRZCKICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:03:50.463620Z"},"content_sha256":"83bffce6ab91444eb344e631c8f1b1e72c182881e1fb676877eb0d8043b202a7","schema_version":"1.0","event_id":"sha256:83bffce6ab91444eb344e631c8f1b1e72c182881e1fb676877eb0d8043b202a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJE6YFYVA7LGL23RUERYDOYENW/bundle.json","state_url":"https://pith.science/pith/OJE6YFYVA7LGL23RUERYDOYENW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJE6YFYVA7LGL23RUERYDOYENW/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":"2026-06-10T07:03:50Z","links":{"resolver":"https://pith.science/pith/OJE6YFYVA7LGL23RUERYDOYENW","bundle":"https://pith.science/pith/OJE6YFYVA7LGL23RUERYDOYENW/bundle.json","state":"https://pith.science/pith/OJE6YFYVA7LGL23RUERYDOYENW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJE6YFYVA7LGL23RUERYDOYENW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OJE6YFYVA7LGL23RUERYDOYENW","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":"20d21fb5cfa0fc43102a3aff077fac14bbfc535f22c2debf21783c0b18a98006","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-27T23:35:24Z","title_canon_sha256":"68a19e9c389869d8acaae1045a39a64591a8ea73a2811fa23e130f12f441a48f"},"schema_version":"1.0","source":{"id":"1203.6113","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6113","created_at":"2026-05-18T03:59:04Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6113v1","created_at":"2026-05-18T03:59:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6113","created_at":"2026-05-18T03:59:04Z"},{"alias_kind":"pith_short_12","alias_value":"OJE6YFYVA7LG","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OJE6YFYVA7LGL23R","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OJE6YFYV","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:83bffce6ab91444eb344e631c8f1b1e72c182881e1fb676877eb0d8043b202a7","target":"graph","created_at":"2026-05-18T03:59:04Z","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":"Singular Riemannian Foliations are particular types of foliations on Riemannian manifolds, in which leaves locally stay at a constant distance from each other. Singular Riemannian Foliations in round spheres play a special role, since they provide \"infinitesimal information\" about general Singular Riemannian Foliations. In this paper we show that Singular Riemannian Foliations in spheres, of dimension at most 3, are orbits of an isometric group action.","authors_text":"Marco Radeschi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-27T23:35:24Z","title":"Low dimensional Singular Riemannian Foliations in spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6113","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":"sha256:0be66d02af59ff420c5e770eae74b9a8e2e6521962c9856e93fbf2ee95e8ad47","target":"record","created_at":"2026-05-18T03:59:04Z","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":"20d21fb5cfa0fc43102a3aff077fac14bbfc535f22c2debf21783c0b18a98006","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-27T23:35:24Z","title_canon_sha256":"68a19e9c389869d8acaae1045a39a64591a8ea73a2811fa23e130f12f441a48f"},"schema_version":"1.0","source":{"id":"1203.6113","kind":"arxiv","version":1}},"canonical_sha256":"7249ec171507d665eb71a12381bb046db431f992a744a795e8ba67667ef6849d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7249ec171507d665eb71a12381bb046db431f992a744a795e8ba67667ef6849d","first_computed_at":"2026-05-18T03:59:04.127442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:04.127442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Jz+W2LKBsYjMizVZDCKlJfrEqDnh4cRB0DU3reUA5LUFdLIXAdBAywFbbTsImr8m+0l72mG4gq8S26WqF5fCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:04.128278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6113","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0be66d02af59ff420c5e770eae74b9a8e2e6521962c9856e93fbf2ee95e8ad47","sha256:83bffce6ab91444eb344e631c8f1b1e72c182881e1fb676877eb0d8043b202a7"],"state_sha256":"66ee9a36423398dfe0f08711ec8e8e19e3eeb6f5cdfb6188cbc09302488fc71f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UXXSfW047MvwU4P4z4CR2txJvfVKFE+NbexVFbVfruRmDKYUuEk7tpdROSxePs/j+UHKVet2e721/DwvXCZcAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T07:03:50.466825Z","bundle_sha256":"a2302fc19ac7cb313614a8b60f0a3ef2514ff03feb494120a77e54ae5bc2f1dd"}}