{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:JQXTYYYIECDMNONJES6ROTI7YP","short_pith_number":"pith:JQXTYYYI","schema_version":"1.0","canonical_sha256":"4c2f3c63082086c6b9a924bd174d1fc3fb2641c4b68d65a64b73e6071fb8be02","source":{"kind":"arxiv","id":"1809.01861","version":1},"attestation_state":"computed","paper":{"title":"On number fields with $k$-free discriminants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Joachim K\\\"onig","submitted_at":"2018-09-06T07:46:49Z","abstract_excerpt":"Given a finite transitive permutation group $G$, we investigate number fields $F/\\mathbb{Q}$ of Galois group $G$ whose discriminant is only divisible by small prime powers. This generalizes previous investigations of number fields with squarefree discriminant. In particular, we obtain a comprehensive result on number fields with cubefree discriminant. Our main tools are arithmetic-geometric, involving in particular an effective criterion on ramification in specializations of Galois covers."},"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":"1809.01861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-06T07:46:49Z","cross_cats_sorted":[],"title_canon_sha256":"457790cf25c49b6015d0a345d1ad21be1e45801842b96cf5bff19885f085d00d","abstract_canon_sha256":"c6f9c240af2a23fab574d368c09c00ecb4fac6fe664d98189c6031b5c21feed7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:21.771437Z","signature_b64":"Fln6S4NLMQcFIf1CWy3u4wRZVa8OEdZyyvl5dWKeUwYui2gRFNKsUw9lGI4fFgAPmaLThJSx3l6b//fmFgk+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c2f3c63082086c6b9a924bd174d1fc3fb2641c4b68d65a64b73e6071fb8be02","last_reissued_at":"2026-05-18T00:06:21.771031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:21.771031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On number fields with $k$-free discriminants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Joachim K\\\"onig","submitted_at":"2018-09-06T07:46:49Z","abstract_excerpt":"Given a finite transitive permutation group $G$, we investigate number fields $F/\\mathbb{Q}$ of Galois group $G$ whose discriminant is only divisible by small prime powers. This generalizes previous investigations of number fields with squarefree discriminant. In particular, we obtain a comprehensive result on number fields with cubefree discriminant. Our main tools are arithmetic-geometric, involving in particular an effective criterion on ramification in specializations of Galois covers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01861","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":"1809.01861","created_at":"2026-05-18T00:06:21.771112+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.01861v1","created_at":"2026-05-18T00:06:21.771112+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01861","created_at":"2026-05-18T00:06:21.771112+00:00"},{"alias_kind":"pith_short_12","alias_value":"JQXTYYYIECDM","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"JQXTYYYIECDMNONJ","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"JQXTYYYI","created_at":"2026-05-18T12:32:31.084164+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/JQXTYYYIECDMNONJES6ROTI7YP","json":"https://pith.science/pith/JQXTYYYIECDMNONJES6ROTI7YP.json","graph_json":"https://pith.science/api/pith-number/JQXTYYYIECDMNONJES6ROTI7YP/graph.json","events_json":"https://pith.science/api/pith-number/JQXTYYYIECDMNONJES6ROTI7YP/events.json","paper":"https://pith.science/paper/JQXTYYYI"},"agent_actions":{"view_html":"https://pith.science/pith/JQXTYYYIECDMNONJES6ROTI7YP","download_json":"https://pith.science/pith/JQXTYYYIECDMNONJES6ROTI7YP.json","view_paper":"https://pith.science/paper/JQXTYYYI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.01861&json=true","fetch_graph":"https://pith.science/api/pith-number/JQXTYYYIECDMNONJES6ROTI7YP/graph.json","fetch_events":"https://pith.science/api/pith-number/JQXTYYYIECDMNONJES6ROTI7YP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JQXTYYYIECDMNONJES6ROTI7YP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JQXTYYYIECDMNONJES6ROTI7YP/action/storage_attestation","attest_author":"https://pith.science/pith/JQXTYYYIECDMNONJES6ROTI7YP/action/author_attestation","sign_citation":"https://pith.science/pith/JQXTYYYIECDMNONJES6ROTI7YP/action/citation_signature","submit_replication":"https://pith.science/pith/JQXTYYYIECDMNONJES6ROTI7YP/action/replication_record"}},"created_at":"2026-05-18T00:06:21.771112+00:00","updated_at":"2026-05-18T00:06:21.771112+00:00"}