{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:RWMSHKCAL4T6Y5AMZGEGWYTLY7","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":"9dd0bc15d596c9f95cf73e624237783eec83d30b37b08a8edb8f55ae1faeab42","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-06T00:45:58Z","title_canon_sha256":"3d59524fce2fa37a5efaa961960c6066f5218af62d62f04e90e9248a4ad269af"},"schema_version":"1.0","source":{"id":"0907.0903","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0903","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0903v1","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0903","created_at":"2026-05-18T04:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"RWMSHKCAL4T6","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"RWMSHKCAL4T6Y5AM","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"RWMSHKCA","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:141a9bcf83ab2951d89a7febb617dbe0f0a687f57d15e9db90c22bc6f9c87165","target":"graph","created_at":"2026-05-18T04:18:23Z","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":"Consider a singular Riemannian foliation (s.r.f for short) on a compact manifold. By successive blow-ups along the strata, we construct a regular Riemannian foliation on another compact Riemannian manifold and a desingularization map that projects leaves of the regular Riemannian foliation into leaves of the s.r.f. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of the s.r.f are compact, then, for each small epsilon, the","authors_text":"Marcos M. Alexandrino","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-06T00:45:58Z","title":"Desingularization of singular Riemannian foliation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0903","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:ca7d997c2e9fa78825a220ffc19f1683700f09104a50ceb40e38ba53a2fd428b","target":"record","created_at":"2026-05-18T04:18:23Z","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":"9dd0bc15d596c9f95cf73e624237783eec83d30b37b08a8edb8f55ae1faeab42","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-06T00:45:58Z","title_canon_sha256":"3d59524fce2fa37a5efaa961960c6066f5218af62d62f04e90e9248a4ad269af"},"schema_version":"1.0","source":{"id":"0907.0903","kind":"arxiv","version":1}},"canonical_sha256":"8d9923a8405f27ec740cc9886b626bc7c00b680002f476d4a92dcfa5b52dd670","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d9923a8405f27ec740cc9886b626bc7c00b680002f476d4a92dcfa5b52dd670","first_computed_at":"2026-05-18T04:18:23.841581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:23.841581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nt1WgHwd/chPIMLGQN3nS5bqTRIXsznO+2KuyN1kZNLkcGOBFqdP6raKsWy0tXzXm9Xss8XFptrAYSNU2DB8Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:23.841972Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0903","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca7d997c2e9fa78825a220ffc19f1683700f09104a50ceb40e38ba53a2fd428b","sha256:141a9bcf83ab2951d89a7febb617dbe0f0a687f57d15e9db90c22bc6f9c87165"],"state_sha256":"19b9b7ae60340030cc1e448f4f899e141f29646c335535a305fa2472ac4ac715"}