{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2Z4PTEYETQLO3723ZL2GD5FXOO","short_pith_number":"pith:2Z4PTEYE","schema_version":"1.0","canonical_sha256":"d678f993049c16edff5bcaf461f4b773ab57c9d969cdd52368cbf5f83604ba8f","source":{"kind":"arxiv","id":"1811.02206","version":1},"attestation_state":"computed","paper":{"title":"Zero-dimensional isomorphic dynamical models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lei Jin, Tomasz Downarowicz, Wolfgang Lusky, Yixiao Qiao","submitted_at":"2018-11-06T07:43:47Z","abstract_excerpt":"By an \\emph{assignment} we mean a mapping from a Choquet simplex $K$ to probability measure-preserving systems, obeying some natural restrictions. We prove that if $\\Phi$ is an aperiodic assignment on a Choquet simplex $K$ such that the set of extreme points $\\mathsf{ex}K$ is a countable union $\\bigcup_n E_n$, where each set $E_n$ is compact, zero-dimensional, and the restriction of $\\Phi$ to the Bauer simplex $K_n$ spanned by $E_n$ can be `embedded' in some topological dynamical system, then $\\Phi$ can be `realized' in a zero-dimensional system."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.02206","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-06T07:43:47Z","cross_cats_sorted":[],"title_canon_sha256":"930d2bc915ee9c867497a16feff5409839318a55b76fbbcf9f9f05f214dd1a64","abstract_canon_sha256":"6e08bcfdebed746681b43267cb681a68c095d33ec3ff33c7a46617e33179ab62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:24.831641Z","signature_b64":"q74TWK6GXnR5e96Sb8/24GKnvqHIfxGmDTeS9nccyfKDSqkl+RydPBEv8I/qsdnfKBwj3SD2pYtGJvUzRt4hAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d678f993049c16edff5bcaf461f4b773ab57c9d969cdd52368cbf5f83604ba8f","last_reissued_at":"2026-05-18T00:01:24.831222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:24.831222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zero-dimensional isomorphic dynamical models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lei Jin, Tomasz Downarowicz, Wolfgang Lusky, Yixiao Qiao","submitted_at":"2018-11-06T07:43:47Z","abstract_excerpt":"By an \\emph{assignment} we mean a mapping from a Choquet simplex $K$ to probability measure-preserving systems, obeying some natural restrictions. We prove that if $\\Phi$ is an aperiodic assignment on a Choquet simplex $K$ such that the set of extreme points $\\mathsf{ex}K$ is a countable union $\\bigcup_n E_n$, where each set $E_n$ is compact, zero-dimensional, and the restriction of $\\Phi$ to the Bauer simplex $K_n$ spanned by $E_n$ can be `embedded' in some topological dynamical system, then $\\Phi$ can be `realized' in a zero-dimensional system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02206","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.02206","created_at":"2026-05-18T00:01:24.831277+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.02206v1","created_at":"2026-05-18T00:01:24.831277+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02206","created_at":"2026-05-18T00:01:24.831277+00:00"},{"alias_kind":"pith_short_12","alias_value":"2Z4PTEYETQLO","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2Z4PTEYETQLO3723","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2Z4PTEYE","created_at":"2026-05-18T12:32:02.567920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2Z4PTEYETQLO3723ZL2GD5FXOO","json":"https://pith.science/pith/2Z4PTEYETQLO3723ZL2GD5FXOO.json","graph_json":"https://pith.science/api/pith-number/2Z4PTEYETQLO3723ZL2GD5FXOO/graph.json","events_json":"https://pith.science/api/pith-number/2Z4PTEYETQLO3723ZL2GD5FXOO/events.json","paper":"https://pith.science/paper/2Z4PTEYE"},"agent_actions":{"view_html":"https://pith.science/pith/2Z4PTEYETQLO3723ZL2GD5FXOO","download_json":"https://pith.science/pith/2Z4PTEYETQLO3723ZL2GD5FXOO.json","view_paper":"https://pith.science/paper/2Z4PTEYE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.02206&json=true","fetch_graph":"https://pith.science/api/pith-number/2Z4PTEYETQLO3723ZL2GD5FXOO/graph.json","fetch_events":"https://pith.science/api/pith-number/2Z4PTEYETQLO3723ZL2GD5FXOO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2Z4PTEYETQLO3723ZL2GD5FXOO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2Z4PTEYETQLO3723ZL2GD5FXOO/action/storage_attestation","attest_author":"https://pith.science/pith/2Z4PTEYETQLO3723ZL2GD5FXOO/action/author_attestation","sign_citation":"https://pith.science/pith/2Z4PTEYETQLO3723ZL2GD5FXOO/action/citation_signature","submit_replication":"https://pith.science/pith/2Z4PTEYETQLO3723ZL2GD5FXOO/action/replication_record"}},"created_at":"2026-05-18T00:01:24.831277+00:00","updated_at":"2026-05-18T00:01:24.831277+00:00"}