{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HNX6M7ENQAXNHKELXGUHN6RTXX","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":"5b85670e4127c3c354e6a51ce31ab3aa0ab87126ca52b17728639d1b04826f37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-20T18:21:53Z","title_canon_sha256":"6f08545e70a933c89cdce0ba48d85988e4c01b38955e92a1a419cc827d7350eb"},"schema_version":"1.0","source":{"id":"1008.3549","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3549","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3549v2","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3549","created_at":"2026-05-18T02:42:15Z"},{"alias_kind":"pith_short_12","alias_value":"HNX6M7ENQAXN","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HNX6M7ENQAXNHKEL","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HNX6M7EN","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:c2608e1f6a8bf23e6b36a2dd85d2694bcdffe342b7fa2b85bdf61d63b2fab95e","target":"graph","created_at":"2026-05-18T02:42:15Z","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":"A Borel system consists of a measurable automorphism of a standard Borel space. We consider Borel embeddings and isomorphisms between such systems modulo null sets, i.e. sets which have measure zero for every invariant probability measure. For every t>0 we show that in this category there exists a unique free Borel system (Y,S) which is strictly t-universal in the sense that all invariant measures on Y have entropy <t, and if (X,T) is another free system obeying the same entropy condition then X embeds into Y off a null set. One gets a strictly t-universal system from mixing shifts of finite t","authors_text":"Michael Hochman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-20T18:21:53Z","title":"Isomorphism and embedding of Borel systems on full sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3549","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":"sha256:3dc8b74935a8028d31c158a1ca29624fe7f5b419934b0d3b140322de683e61e4","target":"record","created_at":"2026-05-18T02:42:15Z","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":"5b85670e4127c3c354e6a51ce31ab3aa0ab87126ca52b17728639d1b04826f37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-20T18:21:53Z","title_canon_sha256":"6f08545e70a933c89cdce0ba48d85988e4c01b38955e92a1a419cc827d7350eb"},"schema_version":"1.0","source":{"id":"1008.3549","kind":"arxiv","version":2}},"canonical_sha256":"3b6fe67c8d802ed3a88bb9a876fa33bdf7ded4963a08ae38ab96c6909e002f3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b6fe67c8d802ed3a88bb9a876fa33bdf7ded4963a08ae38ab96c6909e002f3c","first_computed_at":"2026-05-18T02:42:15.477501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:15.477501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2VlMtdjIEfD82cB7DI6kjCBiMZQ+TZ+MDLvKcVUROabQ4GX+pK5qmryyyyK8ksvymiACiRRzDhMh20PWfcSsDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:15.478171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3549","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dc8b74935a8028d31c158a1ca29624fe7f5b419934b0d3b140322de683e61e4","sha256:c2608e1f6a8bf23e6b36a2dd85d2694bcdffe342b7fa2b85bdf61d63b2fab95e"],"state_sha256":"925eaff7590f3ecf2e613d0e4dad3aff9fb6c6d3d95d1facd71aa0a594458ec8"}