{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZEXCTHTPCQIEIFQVXVOJVPPRD5","short_pith_number":"pith:ZEXCTHTP","schema_version":"1.0","canonical_sha256":"c92e299e6f1410441615bd5c9abdf11f46b0e9deef0eab9ea0bda91c750f5323","source":{"kind":"arxiv","id":"1704.01729","version":1},"attestation_state":"computed","paper":{"title":"The number of quartic $D_4$-fields ordered by conductor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Arul Shankar, Ila Varma, Kevin H. Wilson, Salim Ali Altug","submitted_at":"2017-04-06T07:27:10Z","abstract_excerpt":"We consider families of number fields of degree 4 whose normal closures over $\\mathbb{Q}$ have Galois group isomorphic to $D_4$, the symmetries of a square. To any such field $L$, one can associate the Artin conductor of the corresponding 2-dimensional irreducible Galois representation with image $D_4$. We determine the asymptotic number of such quartic $D_4$-fields ordered by conductor, and compute the leading term explicitly as a mass formula, verifying heuristics of Kedlaya and Wood. Additionally, we are able to impose any local splitting conditions at any finite number of primes (sometimes"},"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":"1704.01729","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-06T07:27:10Z","cross_cats_sorted":[],"title_canon_sha256":"0582df1da7647a8a2aa5dc74c7b0889c1607d072c1e1bc3b849aec23414f2a81","abstract_canon_sha256":"3c87380cc35c99085d2f833688f1c8547115900b8724122b18180cc35a9ae2e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:54.454444Z","signature_b64":"hAb69yRK74f1q/f0w/bdlVm6nmdbFjHiCVOqFEt6VGlJ+PthGmCQ80vGh+MX/ZxnuGU1lcs8AVQP9pkbUVajCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c92e299e6f1410441615bd5c9abdf11f46b0e9deef0eab9ea0bda91c750f5323","last_reissued_at":"2026-05-18T00:46:54.453826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:54.453826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The number of quartic $D_4$-fields ordered by conductor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Arul Shankar, Ila Varma, Kevin H. Wilson, Salim Ali Altug","submitted_at":"2017-04-06T07:27:10Z","abstract_excerpt":"We consider families of number fields of degree 4 whose normal closures over $\\mathbb{Q}$ have Galois group isomorphic to $D_4$, the symmetries of a square. To any such field $L$, one can associate the Artin conductor of the corresponding 2-dimensional irreducible Galois representation with image $D_4$. We determine the asymptotic number of such quartic $D_4$-fields ordered by conductor, and compute the leading term explicitly as a mass formula, verifying heuristics of Kedlaya and Wood. Additionally, we are able to impose any local splitting conditions at any finite number of primes (sometimes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01729","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":"1704.01729","created_at":"2026-05-18T00:46:54.453934+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.01729v1","created_at":"2026-05-18T00:46:54.453934+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01729","created_at":"2026-05-18T00:46:54.453934+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZEXCTHTPCQIE","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZEXCTHTPCQIEIFQV","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZEXCTHTP","created_at":"2026-05-18T12:31:59.375834+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/ZEXCTHTPCQIEIFQVXVOJVPPRD5","json":"https://pith.science/pith/ZEXCTHTPCQIEIFQVXVOJVPPRD5.json","graph_json":"https://pith.science/api/pith-number/ZEXCTHTPCQIEIFQVXVOJVPPRD5/graph.json","events_json":"https://pith.science/api/pith-number/ZEXCTHTPCQIEIFQVXVOJVPPRD5/events.json","paper":"https://pith.science/paper/ZEXCTHTP"},"agent_actions":{"view_html":"https://pith.science/pith/ZEXCTHTPCQIEIFQVXVOJVPPRD5","download_json":"https://pith.science/pith/ZEXCTHTPCQIEIFQVXVOJVPPRD5.json","view_paper":"https://pith.science/paper/ZEXCTHTP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.01729&json=true","fetch_graph":"https://pith.science/api/pith-number/ZEXCTHTPCQIEIFQVXVOJVPPRD5/graph.json","fetch_events":"https://pith.science/api/pith-number/ZEXCTHTPCQIEIFQVXVOJVPPRD5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZEXCTHTPCQIEIFQVXVOJVPPRD5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZEXCTHTPCQIEIFQVXVOJVPPRD5/action/storage_attestation","attest_author":"https://pith.science/pith/ZEXCTHTPCQIEIFQVXVOJVPPRD5/action/author_attestation","sign_citation":"https://pith.science/pith/ZEXCTHTPCQIEIFQVXVOJVPPRD5/action/citation_signature","submit_replication":"https://pith.science/pith/ZEXCTHTPCQIEIFQVXVOJVPPRD5/action/replication_record"}},"created_at":"2026-05-18T00:46:54.453934+00:00","updated_at":"2026-05-18T00:46:54.453934+00:00"}