{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VZUGTKC43J6J5YKLNV62CD7UEE","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":"08de2f3ef7d1a327ce0b79f1de2fd56ab8888b20946d9ef8532fff246f12e566","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-08T18:50:08Z","title_canon_sha256":"a8b3a1d7dd0005a91efa32ddbcf9bbf26ecebadc97bfc05c7043fd5da835f0bf"},"schema_version":"1.0","source":{"id":"1507.02252","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02252","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02252v2","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02252","created_at":"2026-05-18T01:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"VZUGTKC43J6J","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VZUGTKC43J6J5YKL","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VZUGTKC4","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:82df13ebd4bed309ecad783da41e8e0ad3c10041b64c38d46173b8b25a0cc79b","target":"graph","created_at":"2026-05-18T01:36:47Z","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":"Any free Borel flow is shown to admit a cross section with only two possible distances between adjacent points. Non smooth flows are proved to be Lebesgue orbit equivalent if and only if they admit the same number of invariant ergodic probability measures.","authors_text":"Konstantin Slutsky","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-08T18:50:08Z","title":"Regular cross sections of Borel flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02252","kind":"arxiv","version":2},"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":"sha256:96e8dc2fdbb97bfdceda163ee2765eb70a52bbaeb77f463ecf55709742c18cdb","target":"record","created_at":"2026-05-18T01:36:47Z","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":"08de2f3ef7d1a327ce0b79f1de2fd56ab8888b20946d9ef8532fff246f12e566","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-08T18:50:08Z","title_canon_sha256":"a8b3a1d7dd0005a91efa32ddbcf9bbf26ecebadc97bfc05c7043fd5da835f0bf"},"schema_version":"1.0","source":{"id":"1507.02252","kind":"arxiv","version":2}},"canonical_sha256":"ae6869a85cda7c9ee14b6d7da10ff42109589ff882e659574c1aba1d426492e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae6869a85cda7c9ee14b6d7da10ff42109589ff882e659574c1aba1d426492e3","first_computed_at":"2026-05-18T01:36:47.678133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:47.678133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XEnul5negHXjYPIfF4fE39wi5ileAH+X7clb5URJ96vew7EhZKEVGE+1TGeVCnawAGxOIAOx054o+Xfeo19sCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:47.678662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02252","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96e8dc2fdbb97bfdceda163ee2765eb70a52bbaeb77f463ecf55709742c18cdb","sha256:82df13ebd4bed309ecad783da41e8e0ad3c10041b64c38d46173b8b25a0cc79b"],"state_sha256":"d15c102c66575e79816e3ff94ff9664cfbc04c683a25f8bdcdc4affb7d7717b6"}