{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3O4VFJATGZ65AB6BAOEFZJQWEC","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":"de2d60b7a7a2049141912e267a7b9f3d39005e59e9158245b65918d236a8e33b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-16T21:44:54Z","title_canon_sha256":"925ff24e3b8424a18803214a580ec1463f31f9f36ef287151a68c776f3a135b1"},"schema_version":"1.0","source":{"id":"1208.3501","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3501","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3501v3","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3501","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"pith_short_12","alias_value":"3O4VFJATGZ65","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3O4VFJATGZ65AB6B","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3O4VFJAT","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:86eaff179a8b22940e53a8980b36f46291eb3931ac8949edd2aa37c7e844c716","target":"graph","created_at":"2026-05-18T02:49:46Z","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":"The Krieger generator theorem says that every invertible ergodic measure-preserving system with finite measure-theoretic entropy can be embedded into a full shift with strictly greater topological entropy. We extend Krieger's theorem to include toral automorphisms, and more generally, any topological dynamical system on a compact metric space that satisfies almost weak specification, asymptotic entropy expansiveness, and the small boundary property. As a corollary, one obtains a complete solution to a natural generalization of an open problem in Halmos's 1956 book regarding an isomorphism inva","authors_text":"Anthony Quas, Terry Soo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-16T21:44:54Z","title":"Ergodic universality of some topological dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3501","kind":"arxiv","version":3},"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":"sha256:7bf80b3a3a86ad80259434b1b129edd70fb88b07d6384f1457f4949f6765ec00","target":"record","created_at":"2026-05-18T02:49:46Z","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":"de2d60b7a7a2049141912e267a7b9f3d39005e59e9158245b65918d236a8e33b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-08-16T21:44:54Z","title_canon_sha256":"925ff24e3b8424a18803214a580ec1463f31f9f36ef287151a68c776f3a135b1"},"schema_version":"1.0","source":{"id":"1208.3501","kind":"arxiv","version":3}},"canonical_sha256":"dbb952a413367dd007c103885ca61620885391e206bd8f134c8770af96ff9282","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbb952a413367dd007c103885ca61620885391e206bd8f134c8770af96ff9282","first_computed_at":"2026-05-18T02:49:46.209036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:46.209036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IamM+NQYVN4ahjKMHV2DUNoM5O3rCblg4utEvaJ8PrAoHmJ5gtbVIxFnr/3+LR5kMZUktP+rGF7v1xKY3+WPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:46.209446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3501","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bf80b3a3a86ad80259434b1b129edd70fb88b07d6384f1457f4949f6765ec00","sha256:86eaff179a8b22940e53a8980b36f46291eb3931ac8949edd2aa37c7e844c716"],"state_sha256":"2876a2c76e6aadf1dd28bf2b7a42c41029fded1cfd0491b86039cd23a77fd7e2"}