{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:Y4KQOPLZ6435AXJ2MQXWQ7576Q","short_pith_number":"pith:Y4KQOPLZ","schema_version":"1.0","canonical_sha256":"c715073d79f737d05d3a642f687fbff43d5db173ae7daef4048627b966f539bc","source":{"kind":"arxiv","id":"1901.01088","version":1},"attestation_state":"computed","paper":{"title":"Dynamics of the $a$-map over residually finite Dedekind Domains and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Claudio Qureshi, Lucas Reis","submitted_at":"2019-01-04T13:39:35Z","abstract_excerpt":"Let $\\mathfrak D$ be a residually finite Dedekind domain, $a\\in \\mathfrak D$ be a nonzero element and $\\mathfrak n$ be a nonzero ideal of $\\mathfrak D$. In this paper we describe the dynamics of the map $x\\mapsto ax$ over the quotient ring $\\mathfrak D/\\mathfrak n$. We further present some applications of our main result."},"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":"1901.01088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-04T13:39:35Z","cross_cats_sorted":[],"title_canon_sha256":"2f2b95c66048b4bd0ac2fa0db58f9a7103b77fdd1ae4aa1fd2cdb7231013905c","abstract_canon_sha256":"e08db038413ca6eb3e3e40310680367bde4974816d6b29fbc012244d904ea458"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:57.128675Z","signature_b64":"dLrkFwORBMa3kQZif+o10YKhti2pverwuHA3mjh+WbXDkWJrSm7FMR7UCiBBbUJ9DDi4+rd+e+1NficMvIl3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c715073d79f737d05d3a642f687fbff43d5db173ae7daef4048627b966f539bc","last_reissued_at":"2026-05-17T23:56:57.128053Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:57.128053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of the $a$-map over residually finite Dedekind Domains and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Claudio Qureshi, Lucas Reis","submitted_at":"2019-01-04T13:39:35Z","abstract_excerpt":"Let $\\mathfrak D$ be a residually finite Dedekind domain, $a\\in \\mathfrak D$ be a nonzero element and $\\mathfrak n$ be a nonzero ideal of $\\mathfrak D$. In this paper we describe the dynamics of the map $x\\mapsto ax$ over the quotient ring $\\mathfrak D/\\mathfrak n$. We further present some applications of our main result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01088","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":"1901.01088","created_at":"2026-05-17T23:56:57.128151+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.01088v1","created_at":"2026-05-17T23:56:57.128151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01088","created_at":"2026-05-17T23:56:57.128151+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y4KQOPLZ6435","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y4KQOPLZ6435AXJ2","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y4KQOPLZ","created_at":"2026-05-18T12:33:33.725879+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/Y4KQOPLZ6435AXJ2MQXWQ7576Q","json":"https://pith.science/pith/Y4KQOPLZ6435AXJ2MQXWQ7576Q.json","graph_json":"https://pith.science/api/pith-number/Y4KQOPLZ6435AXJ2MQXWQ7576Q/graph.json","events_json":"https://pith.science/api/pith-number/Y4KQOPLZ6435AXJ2MQXWQ7576Q/events.json","paper":"https://pith.science/paper/Y4KQOPLZ"},"agent_actions":{"view_html":"https://pith.science/pith/Y4KQOPLZ6435AXJ2MQXWQ7576Q","download_json":"https://pith.science/pith/Y4KQOPLZ6435AXJ2MQXWQ7576Q.json","view_paper":"https://pith.science/paper/Y4KQOPLZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.01088&json=true","fetch_graph":"https://pith.science/api/pith-number/Y4KQOPLZ6435AXJ2MQXWQ7576Q/graph.json","fetch_events":"https://pith.science/api/pith-number/Y4KQOPLZ6435AXJ2MQXWQ7576Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y4KQOPLZ6435AXJ2MQXWQ7576Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y4KQOPLZ6435AXJ2MQXWQ7576Q/action/storage_attestation","attest_author":"https://pith.science/pith/Y4KQOPLZ6435AXJ2MQXWQ7576Q/action/author_attestation","sign_citation":"https://pith.science/pith/Y4KQOPLZ6435AXJ2MQXWQ7576Q/action/citation_signature","submit_replication":"https://pith.science/pith/Y4KQOPLZ6435AXJ2MQXWQ7576Q/action/replication_record"}},"created_at":"2026-05-17T23:56:57.128151+00:00","updated_at":"2026-05-17T23:56:57.128151+00:00"}