{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:USPU7HZVI2DEOWTLEKFGYASXGJ","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":"a51b3f35c1092c3b169c91dd3738b1d83adfbf4511e1745ef0771a048257fc20","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2006-08-02T21:41:28Z","title_canon_sha256":"ad274eb2cab69bfd8f99246eade999f7862be24c906b953a6b6d5de831ebc016"},"schema_version":"1.0","source":{"id":"math/0608069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608069","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608069v1","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608069","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"USPU7HZVI2DE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"USPU7HZVI2DEOWTL","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"USPU7HZV","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:82752a131b57f0bd4e6e99c29fb44f3f4657918469d2162867b59b4dccba8d45","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":"A singular riemannian foliation F on a complete riemannian manifold M is said to admit sections if each regular point of M is contained in a complete totally geodesic immersed submanifold (a section) that meets every leaf of F orthogonally and whose dimension is the codimension of the regular leaves of F.\n  We prove that the algebra of basic forms of M relative to F is isomorphic to the algebra of those differential forms on a section that are invariant under the generalized Weyl pseudogroup of this section. This extends a result of Michor for polar actions. It follows from this result that th","authors_text":"Claudio Gorodski, Marcos Alexandrino","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2006-08-02T21:41:28Z","title":"Singular riemannian foliations with sections, transnormal maps and basic forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608069","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":"sha256:986b75cd97cbe46f7c9c083da680d1e8a647f9b81c5be5f15dc92f556d49bc92","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":"a51b3f35c1092c3b169c91dd3738b1d83adfbf4511e1745ef0771a048257fc20","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2006-08-02T21:41:28Z","title_canon_sha256":"ad274eb2cab69bfd8f99246eade999f7862be24c906b953a6b6d5de831ebc016"},"schema_version":"1.0","source":{"id":"math/0608069","kind":"arxiv","version":1}},"canonical_sha256":"a49f4f9f354686475a6b228a6c025732411c27c159dff5ad0619aab6d3b06004","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a49f4f9f354686475a6b228a6c025732411c27c159dff5ad0619aab6d3b06004","first_computed_at":"2026-05-18T04:19:41.440611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:41.440611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fx7k7eEY/XhePGDVDBu5jMjpOnic4ZNx7cMJkd7P85JjbrNOlUE+mWUffqLedAmgxwGUJz7ibh6Azfzod9RLAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:41.441174Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0608069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:986b75cd97cbe46f7c9c083da680d1e8a647f9b81c5be5f15dc92f556d49bc92","sha256:82752a131b57f0bd4e6e99c29fb44f3f4657918469d2162867b59b4dccba8d45"],"state_sha256":"d0deb5e77e923bf617733baa3521a01485411ac9cea4e06d0f482286079858ef"}