{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AVJJFVXCFPI2KVLUWHKJPLU5NS","short_pith_number":"pith:AVJJFVXC","schema_version":"1.0","canonical_sha256":"055292d6e22bd1a55574b1d497ae9d6cb8df88fc7d0190b1d4fe849619560001","source":{"kind":"arxiv","id":"1604.02638","version":2},"attestation_state":"computed","paper":{"title":"Totally Rank One Interval Exchange Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Diquan Li, Dongmei Li, Yue Wu, Yunjian Wang","submitted_at":"2016-04-10T05:02:52Z","abstract_excerpt":"For irreducible interval exchange transformations, we study the relation between the powers of induced map and the induced maps of powers and raise a condition of equivalence between them. And skew production of Rauzy induction map is set up and verified to be ergodic regard to a product measure. Then we prove that almost all the interval exchange transformations are totally rank one (rank one for all powers of positive integers) by interval. As a corollary, for almost all interval exchange transformations, rank one transformations are dense $G_{\\delta}$ in the weak closure."},"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":"1604.02638","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-10T05:02:52Z","cross_cats_sorted":[],"title_canon_sha256":"5a99b1cce9b5f47cde8980def36a438d4b83bf4cb9c0296fbcef20b371aa237e","abstract_canon_sha256":"179f7ed441bb236af87f5c401e9b3dcb829fda52f0b90361a22ec64c6a93abb1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:23.316111Z","signature_b64":"+OK40f8XC3Z3rtv/9aTcvNCeIpn3/KtMcavegWpwHTSH5qU6jA96PhO/F9RGI+OuLOZiJcreRjLXapDJia86Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"055292d6e22bd1a55574b1d497ae9d6cb8df88fc7d0190b1d4fe849619560001","last_reissued_at":"2026-05-18T01:10:23.315519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:23.315519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Totally Rank One Interval Exchange Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Diquan Li, Dongmei Li, Yue Wu, Yunjian Wang","submitted_at":"2016-04-10T05:02:52Z","abstract_excerpt":"For irreducible interval exchange transformations, we study the relation between the powers of induced map and the induced maps of powers and raise a condition of equivalence between them. And skew production of Rauzy induction map is set up and verified to be ergodic regard to a product measure. Then we prove that almost all the interval exchange transformations are totally rank one (rank one for all powers of positive integers) by interval. As a corollary, for almost all interval exchange transformations, rank one transformations are dense $G_{\\delta}$ in the weak closure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02638","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":"1604.02638","created_at":"2026-05-18T01:10:23.315675+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.02638v2","created_at":"2026-05-18T01:10:23.315675+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02638","created_at":"2026-05-18T01:10:23.315675+00:00"},{"alias_kind":"pith_short_12","alias_value":"AVJJFVXCFPI2","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AVJJFVXCFPI2KVLU","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AVJJFVXC","created_at":"2026-05-18T12:30:07.202191+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/AVJJFVXCFPI2KVLUWHKJPLU5NS","json":"https://pith.science/pith/AVJJFVXCFPI2KVLUWHKJPLU5NS.json","graph_json":"https://pith.science/api/pith-number/AVJJFVXCFPI2KVLUWHKJPLU5NS/graph.json","events_json":"https://pith.science/api/pith-number/AVJJFVXCFPI2KVLUWHKJPLU5NS/events.json","paper":"https://pith.science/paper/AVJJFVXC"},"agent_actions":{"view_html":"https://pith.science/pith/AVJJFVXCFPI2KVLUWHKJPLU5NS","download_json":"https://pith.science/pith/AVJJFVXCFPI2KVLUWHKJPLU5NS.json","view_paper":"https://pith.science/paper/AVJJFVXC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.02638&json=true","fetch_graph":"https://pith.science/api/pith-number/AVJJFVXCFPI2KVLUWHKJPLU5NS/graph.json","fetch_events":"https://pith.science/api/pith-number/AVJJFVXCFPI2KVLUWHKJPLU5NS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AVJJFVXCFPI2KVLUWHKJPLU5NS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AVJJFVXCFPI2KVLUWHKJPLU5NS/action/storage_attestation","attest_author":"https://pith.science/pith/AVJJFVXCFPI2KVLUWHKJPLU5NS/action/author_attestation","sign_citation":"https://pith.science/pith/AVJJFVXCFPI2KVLUWHKJPLU5NS/action/citation_signature","submit_replication":"https://pith.science/pith/AVJJFVXCFPI2KVLUWHKJPLU5NS/action/replication_record"}},"created_at":"2026-05-18T01:10:23.315675+00:00","updated_at":"2026-05-18T01:10:23.315675+00:00"}