{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:25RPP4O2WF2WSA6ERPDLXSKEFV","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":"b8c28c195b4da39e6fc23b00c4e63519d40be7751874193747df3db15d3911b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-10T17:58:32Z","title_canon_sha256":"5293a03d6f8a5844d9160ce85c699841715f42ded72d545436ebd2043c8b9c62"},"schema_version":"1.0","source":{"id":"1508.02335","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02335","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02335v2","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02335","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"pith_short_12","alias_value":"25RPP4O2WF2W","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"25RPP4O2WF2WSA6E","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"25RPP4O2","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:bd988538c7f256b72f0582ece3fe5ab261d345f6623b0874874c9853040ac31e","target":"graph","created_at":"2026-05-18T00:43:03Z","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 show that if an automorphism of a standard Borel space does not admit finite invariant measures, then it has a two-set generator modulo the sigma-ideal generated by wandering sets. This implies that if the entropies of invariant probability measures of a Borel system are all less than log(k), then the system admits a k-set generator, and that a wide class of hyperbolic-like systems are classified completely at the Borel level by entropy and periodic points counts.","authors_text":"Michael Hochman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-10T17:58:32Z","title":"Every Borel automorphism without finite invariant measures admits a two-set generator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02335","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":"sha256:167216c51f2e00705274ff4a3b1208158f83b40e8472b190c7788b72ddeab2e0","target":"record","created_at":"2026-05-18T00:43:03Z","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":"b8c28c195b4da39e6fc23b00c4e63519d40be7751874193747df3db15d3911b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-10T17:58:32Z","title_canon_sha256":"5293a03d6f8a5844d9160ce85c699841715f42ded72d545436ebd2043c8b9c62"},"schema_version":"1.0","source":{"id":"1508.02335","kind":"arxiv","version":2}},"canonical_sha256":"d762f7f1dab1756903c48bc6bbc9442d54cb39c032df7616cc8985710689a2b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d762f7f1dab1756903c48bc6bbc9442d54cb39c032df7616cc8985710689a2b4","first_computed_at":"2026-05-18T00:43:03.244170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:03.244170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AOOafFc/oDaDX3SYsPinvjAf2Ac8FsNhCy7AfrkhRykGPFhkHwQ1MCeqrJf7ag0MXFBWHk8ok+gqfBv/1pw+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:03.244797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02335","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:167216c51f2e00705274ff4a3b1208158f83b40e8472b190c7788b72ddeab2e0","sha256:bd988538c7f256b72f0582ece3fe5ab261d345f6623b0874874c9853040ac31e"],"state_sha256":"178912fe3ddeab5b034e9a702d581bcf579f166b9ec4f6102cec73bf109eedda"}