{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:YUBJHKG43YYOCBFC2EHZL5PRUF","short_pith_number":"pith:YUBJHKG4","schema_version":"1.0","canonical_sha256":"c50293a8dcde30e104a2d10f95f5f1a14c8d3e7b2835a4644028d2db89316080","source":{"kind":"arxiv","id":"1604.02597","version":2},"attestation_state":"computed","paper":{"title":"A Family of Totally Rank One Two-sided Shift Maps","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":"2016-04-09T19:19:02Z","abstract_excerpt":"'Generalized del Junco-Rudolph's map', a sub-family of generalized Chacon's map (\\cite{FER1}), is introduced. A skew product related to the structure of the Generalized del Junco-Rudolph's map is introduced. A Relative Prime Relation, $h_{k+1}\\equiv 1 \\mod q$ is verified, based on the proposition of iterations of this skew product. We say a measure-preserving transformation $T$ is totally rank one if $T^{q}$ is rank one for every $q\\in \\mathbb{N}$. In this paper, we show that of every Generalized del Junco-Rudolph's map is totally rank one."},"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":"1604.02597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-09T19:19:02Z","cross_cats_sorted":[],"title_canon_sha256":"32a8fb1ffe5a4907e26418229422c3270b10db8bf1bfee153602af81c4704b94","abstract_canon_sha256":"1752f4efb7ffec2b674f71af4eb605a75e76bc559642939a53d68bb1f1694956"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:23.322679Z","signature_b64":"L/TxMHVwMPfEiSkp2l6GN23I6dUBokmN31JTnHoq/txHTqc817nBis5Iv8NcXr3hL7DL2zrZU4PjUg81QaewBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c50293a8dcde30e104a2d10f95f5f1a14c8d3e7b2835a4644028d2db89316080","last_reissued_at":"2026-05-18T01:10:23.322187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:23.322187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Family of Totally Rank One Two-sided Shift Maps","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":"2016-04-09T19:19:02Z","abstract_excerpt":"'Generalized del Junco-Rudolph's map', a sub-family of generalized Chacon's map (\\cite{FER1}), is introduced. A skew product related to the structure of the Generalized del Junco-Rudolph's map is introduced. A Relative Prime Relation, $h_{k+1}\\equiv 1 \\mod q$ is verified, based on the proposition of iterations of this skew product. We say a measure-preserving transformation $T$ is totally rank one if $T^{q}$ is rank one for every $q\\in \\mathbb{N}$. In this paper, we show that of every Generalized del Junco-Rudolph's map is totally rank one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02597","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":"1604.02597","created_at":"2026-05-18T01:10:23.322269+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.02597v2","created_at":"2026-05-18T01:10:23.322269+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02597","created_at":"2026-05-18T01:10:23.322269+00:00"},{"alias_kind":"pith_short_12","alias_value":"YUBJHKG43YYO","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"YUBJHKG43YYOCBFC","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"YUBJHKG4","created_at":"2026-05-18T12:30:53.716459+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/YUBJHKG43YYOCBFC2EHZL5PRUF","json":"https://pith.science/pith/YUBJHKG43YYOCBFC2EHZL5PRUF.json","graph_json":"https://pith.science/api/pith-number/YUBJHKG43YYOCBFC2EHZL5PRUF/graph.json","events_json":"https://pith.science/api/pith-number/YUBJHKG43YYOCBFC2EHZL5PRUF/events.json","paper":"https://pith.science/paper/YUBJHKG4"},"agent_actions":{"view_html":"https://pith.science/pith/YUBJHKG43YYOCBFC2EHZL5PRUF","download_json":"https://pith.science/pith/YUBJHKG43YYOCBFC2EHZL5PRUF.json","view_paper":"https://pith.science/paper/YUBJHKG4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.02597&json=true","fetch_graph":"https://pith.science/api/pith-number/YUBJHKG43YYOCBFC2EHZL5PRUF/graph.json","fetch_events":"https://pith.science/api/pith-number/YUBJHKG43YYOCBFC2EHZL5PRUF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YUBJHKG43YYOCBFC2EHZL5PRUF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YUBJHKG43YYOCBFC2EHZL5PRUF/action/storage_attestation","attest_author":"https://pith.science/pith/YUBJHKG43YYOCBFC2EHZL5PRUF/action/author_attestation","sign_citation":"https://pith.science/pith/YUBJHKG43YYOCBFC2EHZL5PRUF/action/citation_signature","submit_replication":"https://pith.science/pith/YUBJHKG43YYOCBFC2EHZL5PRUF/action/replication_record"}},"created_at":"2026-05-18T01:10:23.322269+00:00","updated_at":"2026-05-18T01:10:23.322269+00:00"}