{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Y3RSBVLVD5AICI7EVUAALICVCI","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":"556f21f0986a7ca6613fac44c9b7ad025a93c16a3234e9143e64b9c178bfe537","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-07-04T11:14:49Z","title_canon_sha256":"c58a9edf09c0ff12c879c7691a7f4e1ea661958000422562a98cff869236fe4a"},"schema_version":"1.0","source":{"id":"1307.1276","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1276","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1276v7","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1276","created_at":"2026-05-18T01:22:08Z"},{"alias_kind":"pith_short_12","alias_value":"Y3RSBVLVD5AI","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y3RSBVLVD5AICI7E","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y3RSBVLV","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:3dea5cfdb11da57d33be65de1352445c18f697404e5b2e37de8b6ff6bd63e137","target":"graph","created_at":"2026-05-18T01:22:08Z","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":"Molino's description of Riemannian foliations on compact manifolds is generalized to the setting of compact equicontinuous foliated spaces, in the case where the leaves are dense. In particular, a structural local group is associated to such a foliated space. As an application, we obtain a partial generalization of results by Carri\\`ere and Breuillard-Gelander, relating the structural local group to the growth of the leaves.","authors_text":"Jes\\'us A. \\'Alvarez L\\'opez, Manuel F. Moreira Galicia","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-07-04T11:14:49Z","title":"Topological Molino's theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1276","kind":"arxiv","version":7},"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":"sha256:1a1154fe07f49e8c203118c9777356568b111a3ca5f36c8e99e9c292e1c683ce","target":"record","created_at":"2026-05-18T01:22:08Z","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":"556f21f0986a7ca6613fac44c9b7ad025a93c16a3234e9143e64b9c178bfe537","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-07-04T11:14:49Z","title_canon_sha256":"c58a9edf09c0ff12c879c7691a7f4e1ea661958000422562a98cff869236fe4a"},"schema_version":"1.0","source":{"id":"1307.1276","kind":"arxiv","version":7}},"canonical_sha256":"c6e320d5751f408123e4ad0005a05512049136467b3a33a418545c57291ebd3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6e320d5751f408123e4ad0005a05512049136467b3a33a418545c57291ebd3d","first_computed_at":"2026-05-18T01:22:08.855072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:08.855072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kuPxasYY8lkfnWmHly6RtRGiKSmq8JC2pyak6l14j2BxVpNG9ZdC5QvLl9Jpw7gnlJfdH0NrXToErm22/hKyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:08.855629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1276","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a1154fe07f49e8c203118c9777356568b111a3ca5f36c8e99e9c292e1c683ce","sha256:3dea5cfdb11da57d33be65de1352445c18f697404e5b2e37de8b6ff6bd63e137"],"state_sha256":"0ff5429cff14d2ee5359b2e418c16e84e185aefe2568c33e073e020832b9b345"}