{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:QBJQITHQWFKGVKOZOL4JHOHUGU","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":"5e8d04fa210f05bbfa88300b5f8199a518a39e191b03f9f27893de2e5f0c5199","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.DG","submitted_at":"2005-09-18T18:21:55Z","title_canon_sha256":"9cc78433d11a6bc082bacbdd011d34ad07bbac67405369389b83e085a0d937aa"},"schema_version":"1.0","source":{"id":"math/0509405","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0509405","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"math/0509405v1","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509405","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"QBJQITHQWFKG","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"QBJQITHQWFKGVKOZ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"QBJQITHQ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:74c2df8a4f8e58fbc88a921d96ebb8cad3413fbae6cc181be6e1f96f1f939ed3","target":"graph","created_at":"2026-05-18T04:19:41Z","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 prove that if the normal distribution of a singular riemannian foliation is integrable, then each leaf of this normal distribution can be extended to be a complete immersed totally geodesic submanifold (called section) which meets every leaf orthogonally. In addition the set of regular points is open and dense in each section. This result generalizes a result of Boualem and solves a problem inspired by a remark of Palais and Terng and a work of Szenthe about polar actions.\n  We also study the singular holonomy of a singular riemannian foliation with sections (s.r.f.s for short) and in parti","authors_text":"Marcos M. Alexandrino","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2005-09-18T18:21:55Z","title":"Proofs of Conjectures about singular riemannian foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509405","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":"sha256:9b5b47fd1882c23201b25c47d16115ea5cfb87b51f6d0663ac3deebd33943966","target":"record","created_at":"2026-05-18T04:19:41Z","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":"5e8d04fa210f05bbfa88300b5f8199a518a39e191b03f9f27893de2e5f0c5199","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.DG","submitted_at":"2005-09-18T18:21:55Z","title_canon_sha256":"9cc78433d11a6bc082bacbdd011d34ad07bbac67405369389b83e085a0d937aa"},"schema_version":"1.0","source":{"id":"math/0509405","kind":"arxiv","version":1}},"canonical_sha256":"8053044cf0b1546aa9d972f893b8f43500304a184dcd50369c6afcbaf80a5997","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8053044cf0b1546aa9d972f893b8f43500304a184dcd50369c6afcbaf80a5997","first_computed_at":"2026-05-18T04:19:41.449376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:41.449376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+2JImPLCkfrbuIzbjwCTWGk+c8RVLNgPPmjp7RcOxVYzXGV7SPjIrLyJhYfguuAIjA4DenHZ+eFYcE6MpJUoCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:41.449983Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0509405","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b5b47fd1882c23201b25c47d16115ea5cfb87b51f6d0663ac3deebd33943966","sha256:74c2df8a4f8e58fbc88a921d96ebb8cad3413fbae6cc181be6e1f96f1f939ed3"],"state_sha256":"cbe4e0f32e863f4a259413fb2f2a30c08b794e0275df397a80a65813e8faf902"}