{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:BRZZXTULFOCSDLZE56KX24NTK7","short_pith_number":"pith:BRZZXTUL","schema_version":"1.0","canonical_sha256":"0c739bce8b2b8521af24ef957d71b357f0c6d13d9207f22c79066446790bbe00","source":{"kind":"arxiv","id":"1005.1221","version":2},"attestation_state":"computed","paper":{"title":"Real extensions of distal minimal flows and continuous topological ergodic decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gernot Greschonig","submitted_at":"2010-05-07T14:40:38Z","abstract_excerpt":"We prove a structure theorem for topologically recurrent real skew product extensions of distal minimal compact metric flows with a compactly generated Abelian acting group (e.g. $\\Z^d$-flows and $\\R^d$-flows). The main result states that every such extension apart from a coboundary can be represented by a perturbation of a so-called Rokhlin skew product. We obtain as a corollary that the topological ergodic decomposition of the skew product extension into prolongations is continuous and compact with respect to the Fell topology on the hyperspace. The right translation acts minimally on this d"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1005.1221","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-05-07T14:40:38Z","cross_cats_sorted":[],"title_canon_sha256":"35445f6f9124e7522c87a0efc2a35176aa7f07b532b3a288af6ba43e9476568d","abstract_canon_sha256":"330360d7c1b8fbd725e9ad4f783ecf374f5242c28fd721e89cff0048d2342b18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:30.632365Z","signature_b64":"9nPr9KOUl7IdqluDaUwZ3BUkBTLtEo2SXLV7W+s2DM9c3XM6sjSHRnZrG+909S+hsQ9oGYos4gC+sY4+EBZgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c739bce8b2b8521af24ef957d71b357f0c6d13d9207f22c79066446790bbe00","last_reissued_at":"2026-05-18T00:44:30.631836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:30.631836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Real extensions of distal minimal flows and continuous topological ergodic decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gernot Greschonig","submitted_at":"2010-05-07T14:40:38Z","abstract_excerpt":"We prove a structure theorem for topologically recurrent real skew product extensions of distal minimal compact metric flows with a compactly generated Abelian acting group (e.g. $\\Z^d$-flows and $\\R^d$-flows). The main result states that every such extension apart from a coboundary can be represented by a perturbation of a so-called Rokhlin skew product. We obtain as a corollary that the topological ergodic decomposition of the skew product extension into prolongations is continuous and compact with respect to the Fell topology on the hyperspace. The right translation acts minimally on this d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1221","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1005.1221","created_at":"2026-05-18T00:44:30.631909+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.1221v2","created_at":"2026-05-18T00:44:30.631909+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1221","created_at":"2026-05-18T00:44:30.631909+00:00"},{"alias_kind":"pith_short_12","alias_value":"BRZZXTULFOCS","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BRZZXTULFOCSDLZE","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BRZZXTUL","created_at":"2026-05-18T12:26:05.355336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BRZZXTULFOCSDLZE56KX24NTK7","json":"https://pith.science/pith/BRZZXTULFOCSDLZE56KX24NTK7.json","graph_json":"https://pith.science/api/pith-number/BRZZXTULFOCSDLZE56KX24NTK7/graph.json","events_json":"https://pith.science/api/pith-number/BRZZXTULFOCSDLZE56KX24NTK7/events.json","paper":"https://pith.science/paper/BRZZXTUL"},"agent_actions":{"view_html":"https://pith.science/pith/BRZZXTULFOCSDLZE56KX24NTK7","download_json":"https://pith.science/pith/BRZZXTULFOCSDLZE56KX24NTK7.json","view_paper":"https://pith.science/paper/BRZZXTUL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.1221&json=true","fetch_graph":"https://pith.science/api/pith-number/BRZZXTULFOCSDLZE56KX24NTK7/graph.json","fetch_events":"https://pith.science/api/pith-number/BRZZXTULFOCSDLZE56KX24NTK7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BRZZXTULFOCSDLZE56KX24NTK7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BRZZXTULFOCSDLZE56KX24NTK7/action/storage_attestation","attest_author":"https://pith.science/pith/BRZZXTULFOCSDLZE56KX24NTK7/action/author_attestation","sign_citation":"https://pith.science/pith/BRZZXTULFOCSDLZE56KX24NTK7/action/citation_signature","submit_replication":"https://pith.science/pith/BRZZXTULFOCSDLZE56KX24NTK7/action/replication_record"}},"created_at":"2026-05-18T00:44:30.631909+00:00","updated_at":"2026-05-18T00:44:30.631909+00:00"}