{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MWJJA4J6URRO5LXBXEKNMZKQNP","short_pith_number":"pith:MWJJA4J6","schema_version":"1.0","canonical_sha256":"659290713ea462eeaee1b914d665506bdd488497fa54194e583168107e88b9fa","source":{"kind":"arxiv","id":"1207.4527","version":2},"attestation_state":"computed","paper":{"title":"Topological isomorphism for rank-1 systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.DS","authors_text":"Aaron Hill, Su Gao","submitted_at":"2012-07-19T00:41:19Z","abstract_excerpt":"We define the Polish space $\\mathcal{R}$ of non-degenerate rank-1 systems. Each non-degenerate rank-1 system can be viewed as a measure-preserving transformation of an atomless, $\\sigma$-finite measure space and as a homeomorphism of a Cantor space. We completely characterize when two non-degenerate rank-1 systems are topologically isomorphic. We also analyze the complexity of the topological isomorphism relation on $\\mathcal{R}$, showing that it is $F_{\\sigma}$ as a subset of $\\mathcal{R} \\times \\mathcal{R}$ and bi-reducible to $E_0$. We also explicitly describe when a non-degenerate rank-1 s"},"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":"1207.4527","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-19T00:41:19Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"2ba86d438f61146293ada3b15e656dcadfb114a9a5bde645c28341217f911539","abstract_canon_sha256":"167c1d816e16c520e323a31929d9c1b35f32632d2f303dc4972b740bf345920d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:06.709714Z","signature_b64":"En7jBg+LQqDIVcgbTgnwoS4IMYprKhzabBH8YPLicxvPB5brqKUBnTVFuj+xmkanB+VIXrZT7Fhn0+IbrG9UBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"659290713ea462eeaee1b914d665506bdd488497fa54194e583168107e88b9fa","last_reissued_at":"2026-05-18T03:31:06.708854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:06.708854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological isomorphism for rank-1 systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.DS","authors_text":"Aaron Hill, Su Gao","submitted_at":"2012-07-19T00:41:19Z","abstract_excerpt":"We define the Polish space $\\mathcal{R}$ of non-degenerate rank-1 systems. Each non-degenerate rank-1 system can be viewed as a measure-preserving transformation of an atomless, $\\sigma$-finite measure space and as a homeomorphism of a Cantor space. We completely characterize when two non-degenerate rank-1 systems are topologically isomorphic. We also analyze the complexity of the topological isomorphism relation on $\\mathcal{R}$, showing that it is $F_{\\sigma}$ as a subset of $\\mathcal{R} \\times \\mathcal{R}$ and bi-reducible to $E_0$. We also explicitly describe when a non-degenerate rank-1 s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4527","kind":"arxiv","version":2},"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":"1207.4527","created_at":"2026-05-18T03:31:06.708991+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.4527v2","created_at":"2026-05-18T03:31:06.708991+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4527","created_at":"2026-05-18T03:31:06.708991+00:00"},{"alias_kind":"pith_short_12","alias_value":"MWJJA4J6URRO","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MWJJA4J6URRO5LXB","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MWJJA4J6","created_at":"2026-05-18T12:27:14.488303+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/MWJJA4J6URRO5LXBXEKNMZKQNP","json":"https://pith.science/pith/MWJJA4J6URRO5LXBXEKNMZKQNP.json","graph_json":"https://pith.science/api/pith-number/MWJJA4J6URRO5LXBXEKNMZKQNP/graph.json","events_json":"https://pith.science/api/pith-number/MWJJA4J6URRO5LXBXEKNMZKQNP/events.json","paper":"https://pith.science/paper/MWJJA4J6"},"agent_actions":{"view_html":"https://pith.science/pith/MWJJA4J6URRO5LXBXEKNMZKQNP","download_json":"https://pith.science/pith/MWJJA4J6URRO5LXBXEKNMZKQNP.json","view_paper":"https://pith.science/paper/MWJJA4J6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.4527&json=true","fetch_graph":"https://pith.science/api/pith-number/MWJJA4J6URRO5LXBXEKNMZKQNP/graph.json","fetch_events":"https://pith.science/api/pith-number/MWJJA4J6URRO5LXBXEKNMZKQNP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MWJJA4J6URRO5LXBXEKNMZKQNP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MWJJA4J6URRO5LXBXEKNMZKQNP/action/storage_attestation","attest_author":"https://pith.science/pith/MWJJA4J6URRO5LXBXEKNMZKQNP/action/author_attestation","sign_citation":"https://pith.science/pith/MWJJA4J6URRO5LXBXEKNMZKQNP/action/citation_signature","submit_replication":"https://pith.science/pith/MWJJA4J6URRO5LXBXEKNMZKQNP/action/replication_record"}},"created_at":"2026-05-18T03:31:06.708991+00:00","updated_at":"2026-05-18T03:31:06.708991+00:00"}