{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JJNZF7QMNSHPVEULP3OD6QTJLG","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":"fb8efc4412539170a186dd097563c7527f39505a4b27112948502635c55add02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-10T09:38:40Z","title_canon_sha256":"9e15b842d843bcf5c6496cd45165dd90ae1831c73e882e734d21fb7ad4c22c08"},"schema_version":"1.0","source":{"id":"1503.02827","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02827","created_at":"2026-05-17T23:54:57Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02827v2","created_at":"2026-05-17T23:54:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02827","created_at":"2026-05-17T23:54:57Z"},{"alias_kind":"pith_short_12","alias_value":"JJNZF7QMNSHP","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JJNZF7QMNSHPVEUL","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JJNZF7QM","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:eb3b33987fcc836d59c41ffef4b6a40a92ddcc4d136a8f724f1bbb89a585fe70","target":"graph","created_at":"2026-05-17T23:54:57Z","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":"We prove that every dynamical system $X$ with free action of a countable amenable group $G$ by homeomorphisms has a zero-dimensional extension $Y$ which is faithful and principal, i.e. every $G$-invariant measure $\\mu$ on $X$ has exactly one preimage $\\nu$ on $Y$ and the conditional entropy of $\\nu$ with respect to $X$ is zero. This is a version of an earlier result by T. Downarowicz and D. Huczek, which establishes the existence of zero-dimensional principal and faithful extensions for general actions of the group of integers.","authors_text":"Dawid Huczek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-10T09:38:40Z","title":"Zero-dimensional extensions of amenable group actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02827","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:f5f7c95aa074d1015b7e431f4fa18e7a7a813bc5274060895721b5f1c1ed7cf3","target":"record","created_at":"2026-05-17T23:54:57Z","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":"fb8efc4412539170a186dd097563c7527f39505a4b27112948502635c55add02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-10T09:38:40Z","title_canon_sha256":"9e15b842d843bcf5c6496cd45165dd90ae1831c73e882e734d21fb7ad4c22c08"},"schema_version":"1.0","source":{"id":"1503.02827","kind":"arxiv","version":2}},"canonical_sha256":"4a5b92fe0c6c8efa928b7edc3f4269598ccd7b2f411a827020c9a4848d1befab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a5b92fe0c6c8efa928b7edc3f4269598ccd7b2f411a827020c9a4848d1befab","first_computed_at":"2026-05-17T23:54:57.217646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:57.217646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wjBU3McEj0TA6/YrzoVZbosAwwpHIIYT9npJMQayf6UV/aoW1aSJYwzUoTjgJIMr+/iDClqpnj/bF2NR1IDfDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:57.218293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02827","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5f7c95aa074d1015b7e431f4fa18e7a7a813bc5274060895721b5f1c1ed7cf3","sha256:eb3b33987fcc836d59c41ffef4b6a40a92ddcc4d136a8f724f1bbb89a585fe70"],"state_sha256":"9dba4579b8c841681f8509ed8057c6a33083e7119a1537b88ed521c6cd9537fc"}