{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:PD2IL6YQ3BZRFN3F2ZNUPQY7K5","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":"79c114fe82b5539480fab83c9ebdf23aefb742b538995980685045e3ed3e7036","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2007-04-24T17:38:58Z","title_canon_sha256":"8fb3445371a93c652f1d6992c57bc1eaadb65625e32ad4ab76a00ed7b8498ce2"},"schema_version":"1.0","source":{"id":"0704.3251","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3251","created_at":"2026-05-18T04:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3251v2","created_at":"2026-05-18T04:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3251","created_at":"2026-05-18T04:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"PD2IL6YQ3BZR","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"PD2IL6YQ3BZRFN3F","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"PD2IL6YQ","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:e1609d47f49e40f0c97f65340c1471776d0801196530d603199ac33b8db42dd4","target":"graph","created_at":"2026-05-18T04:30:26Z","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 on a complete riemannian manifold M is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. We prove that the regular leaves are equifocal, i.e., the end point map of a normal foliated vector field has constant rank. This implies that we can reconstruct the singular foliation by taking all parallel submanifolds of a regular leaf with trivial holonomy. In addition, the end point map of a normal foliated vector field on a leaf with trivial holonomy is a covering map. These results generalize previou","authors_text":"Dirk Toeben, Marcos M. Alexandrino","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2007-04-24T17:38:58Z","title":"Equifocality of a singular riemannian foliation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3251","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:ddcb03d4d8790d75c1cc32c21ea74c8671e1c7e137efcc1539935812762bec46","target":"record","created_at":"2026-05-18T04:30:26Z","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":"79c114fe82b5539480fab83c9ebdf23aefb742b538995980685045e3ed3e7036","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2007-04-24T17:38:58Z","title_canon_sha256":"8fb3445371a93c652f1d6992c57bc1eaadb65625e32ad4ab76a00ed7b8498ce2"},"schema_version":"1.0","source":{"id":"0704.3251","kind":"arxiv","version":2}},"canonical_sha256":"78f485fb10d87312b765d65b47c31f5775f824ec8d4133366209d0f7d9a922d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78f485fb10d87312b765d65b47c31f5775f824ec8d4133366209d0f7d9a922d2","first_computed_at":"2026-05-18T04:30:26.906366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:26.906366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7I1R8SHVkG5EorEjZP7NzVA7L94QZBuVu2X7aa2Qs8rm57RSU3b2/yJ6gT2zGPiBxP57JyZUIO/1kfMVrc3lAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:26.906898Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.3251","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddcb03d4d8790d75c1cc32c21ea74c8671e1c7e137efcc1539935812762bec46","sha256:e1609d47f49e40f0c97f65340c1471776d0801196530d603199ac33b8db42dd4"],"state_sha256":"ca767857644f82324c1b23db58f066c579921b4c9b42b0611dddfc88fd9c2b10"}