{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6KX725CLQXR6GKN7C4FRXQXJ3M","short_pith_number":"pith:6KX725CL","schema_version":"1.0","canonical_sha256":"f2affd744b85e3e329bf170b1bc2e9db1de4df26f1bb26ed44204b82d9dd342c","source":{"kind":"arxiv","id":"1810.04810","version":1},"attestation_state":"computed","paper":{"title":"On Ring Class Fields of Number Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chang Lv, Hairong Yi","submitted_at":"2018-10-11T01:15:12Z","abstract_excerpt":"For a number field $K$, we extend the notion of the ring class field of an order in $K$ [C. Lv and Y. Deng, SciChina. Math., 2015] to that of an arbitrary number ring in $K$. We give both ideal-theoretic and idele-theoretic description of this number ring class field, and characterize it as a subfield of the ring class field of some order. As an application, we use it to give a criterion of the solvability of a higher degree norm form equation over a number ring and finally describe algorithms to compute this field."},"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":"1810.04810","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-11T01:15:12Z","cross_cats_sorted":[],"title_canon_sha256":"8a080a1a07047260e4d7567898fd0799273b58ee9ba8681bbbb87b5cf0a62a5b","abstract_canon_sha256":"2b6161eca27643c43f71345462a19efa8e0a519ff52edb629f0a1696a75d1d93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:35.782418Z","signature_b64":"bxutCVYfpTZKW82ovo0RuikXkireln9MTj0zmY3L92gZMHi3HIRb0J1qVbZjEuNzBvOLh+gSH4DVguXZjdTTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2affd744b85e3e329bf170b1bc2e9db1de4df26f1bb26ed44204b82d9dd342c","last_reissued_at":"2026-05-18T00:03:35.781802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:35.781802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Ring Class Fields of Number Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chang Lv, Hairong Yi","submitted_at":"2018-10-11T01:15:12Z","abstract_excerpt":"For a number field $K$, we extend the notion of the ring class field of an order in $K$ [C. Lv and Y. Deng, SciChina. Math., 2015] to that of an arbitrary number ring in $K$. We give both ideal-theoretic and idele-theoretic description of this number ring class field, and characterize it as a subfield of the ring class field of some order. As an application, we use it to give a criterion of the solvability of a higher degree norm form equation over a number ring and finally describe algorithms to compute this field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04810","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":"1810.04810","created_at":"2026-05-18T00:03:35.781883+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.04810v1","created_at":"2026-05-18T00:03:35.781883+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04810","created_at":"2026-05-18T00:03:35.781883+00:00"},{"alias_kind":"pith_short_12","alias_value":"6KX725CLQXR6","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"6KX725CLQXR6GKN7","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"6KX725CL","created_at":"2026-05-18T12:32:08.215937+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/6KX725CLQXR6GKN7C4FRXQXJ3M","json":"https://pith.science/pith/6KX725CLQXR6GKN7C4FRXQXJ3M.json","graph_json":"https://pith.science/api/pith-number/6KX725CLQXR6GKN7C4FRXQXJ3M/graph.json","events_json":"https://pith.science/api/pith-number/6KX725CLQXR6GKN7C4FRXQXJ3M/events.json","paper":"https://pith.science/paper/6KX725CL"},"agent_actions":{"view_html":"https://pith.science/pith/6KX725CLQXR6GKN7C4FRXQXJ3M","download_json":"https://pith.science/pith/6KX725CLQXR6GKN7C4FRXQXJ3M.json","view_paper":"https://pith.science/paper/6KX725CL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.04810&json=true","fetch_graph":"https://pith.science/api/pith-number/6KX725CLQXR6GKN7C4FRXQXJ3M/graph.json","fetch_events":"https://pith.science/api/pith-number/6KX725CLQXR6GKN7C4FRXQXJ3M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6KX725CLQXR6GKN7C4FRXQXJ3M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6KX725CLQXR6GKN7C4FRXQXJ3M/action/storage_attestation","attest_author":"https://pith.science/pith/6KX725CLQXR6GKN7C4FRXQXJ3M/action/author_attestation","sign_citation":"https://pith.science/pith/6KX725CLQXR6GKN7C4FRXQXJ3M/action/citation_signature","submit_replication":"https://pith.science/pith/6KX725CLQXR6GKN7C4FRXQXJ3M/action/replication_record"}},"created_at":"2026-05-18T00:03:35.781883+00:00","updated_at":"2026-05-18T00:03:35.781883+00:00"}