{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:C6KUJB3QCLZ7BXXHVRBI3I4RYP","short_pith_number":"pith:C6KUJB3Q","schema_version":"1.0","canonical_sha256":"179544877012f3f0dee7ac428da391c3cd58b1f7984e1fee75b9455592e0baea","source":{"kind":"arxiv","id":"2507.12342","version":1},"attestation_state":"computed","paper":{"title":"Counting $D_4$-field extensions by multi-invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anna Zanoli, Willem Hansen","submitted_at":"2025-07-16T15:36:28Z","abstract_excerpt":"We count the number of Galois extensions $M/\\mathbb{Q}$ with fixed Galois group $\\text{Gal}(M/\\mathbb{Q})=D_4$ ordered by multi-invariants introduced by Gundlach. We verify the asymptotic behavior predicted by Gundlach's version of Malle's conjecture. We compare the leading constant to recent predictions by Loughran and Santens."},"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":"2507.12342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-07-16T15:36:28Z","cross_cats_sorted":[],"title_canon_sha256":"ae94ea4a4ad3ccb42d7230e0f82dd2714bd6597bf647fe904c2a311b6dfa89a1","abstract_canon_sha256":"98adb011df414443488dc2c5a960e445b1d77a4765fca6884c0e7d3dc1383469"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:18.612647Z","signature_b64":"v7PPlvvAlXWD80MycfmUzpmu0yeVk9d+XztbY5NmAgGyR7OfZ9Bzawyl8qnkAGaFhzlR/SHNbAX/54yTODNiCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"179544877012f3f0dee7ac428da391c3cd58b1f7984e1fee75b9455592e0baea","last_reissued_at":"2026-07-05T11:38:18.612144Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:18.612144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting $D_4$-field extensions by multi-invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anna Zanoli, Willem Hansen","submitted_at":"2025-07-16T15:36:28Z","abstract_excerpt":"We count the number of Galois extensions $M/\\mathbb{Q}$ with fixed Galois group $\\text{Gal}(M/\\mathbb{Q})=D_4$ ordered by multi-invariants introduced by Gundlach. We verify the asymptotic behavior predicted by Gundlach's version of Malle's conjecture. We compare the leading constant to recent predictions by Loughran and Santens."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12342","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.12342/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.12342","created_at":"2026-07-05T11:38:18.612203+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.12342v1","created_at":"2026-07-05T11:38:18.612203+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12342","created_at":"2026-07-05T11:38:18.612203+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6KUJB3QCLZ7","created_at":"2026-07-05T11:38:18.612203+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6KUJB3QCLZ7BXXH","created_at":"2026-07-05T11:38:18.612203+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6KUJB3Q","created_at":"2026-07-05T11:38:18.612203+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06476","citing_title":"A refined Malle conjecture for Heisenberg groups","ref_index":6,"is_internal_anchor":true},{"citing_arxiv_id":"2606.04983","citing_title":"The leading constant in Malle's conjecture","ref_index":41,"is_internal_anchor":false},{"citing_arxiv_id":"2602.23619","citing_title":"Counting number fields using multiple Dirichlet series","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2511.14576","citing_title":"Non-vanishing of Artin $L$-functions associated with $D_4$-quartic function fields ordered by conductor","ref_index":17,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C6KUJB3QCLZ7BXXHVRBI3I4RYP","json":"https://pith.science/pith/C6KUJB3QCLZ7BXXHVRBI3I4RYP.json","graph_json":"https://pith.science/api/pith-number/C6KUJB3QCLZ7BXXHVRBI3I4RYP/graph.json","events_json":"https://pith.science/api/pith-number/C6KUJB3QCLZ7BXXHVRBI3I4RYP/events.json","paper":"https://pith.science/paper/C6KUJB3Q"},"agent_actions":{"view_html":"https://pith.science/pith/C6KUJB3QCLZ7BXXHVRBI3I4RYP","download_json":"https://pith.science/pith/C6KUJB3QCLZ7BXXHVRBI3I4RYP.json","view_paper":"https://pith.science/paper/C6KUJB3Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.12342&json=true","fetch_graph":"https://pith.science/api/pith-number/C6KUJB3QCLZ7BXXHVRBI3I4RYP/graph.json","fetch_events":"https://pith.science/api/pith-number/C6KUJB3QCLZ7BXXHVRBI3I4RYP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6KUJB3QCLZ7BXXHVRBI3I4RYP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6KUJB3QCLZ7BXXHVRBI3I4RYP/action/storage_attestation","attest_author":"https://pith.science/pith/C6KUJB3QCLZ7BXXHVRBI3I4RYP/action/author_attestation","sign_citation":"https://pith.science/pith/C6KUJB3QCLZ7BXXHVRBI3I4RYP/action/citation_signature","submit_replication":"https://pith.science/pith/C6KUJB3QCLZ7BXXHVRBI3I4RYP/action/replication_record"}},"created_at":"2026-07-05T11:38:18.612203+00:00","updated_at":"2026-07-05T11:38:18.612203+00:00"}