{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:JHPJX2GDYAIZUU45PSF6KPG6PI","short_pith_number":"pith:JHPJX2GD","schema_version":"1.0","canonical_sha256":"49de9be8c3c0119a539d7c8be53cde7a255851ba4ec0ddb2554fe3b31fdc407d","source":{"kind":"arxiv","id":"2211.16698","version":1},"attestation_state":"computed","paper":{"title":"Malle's conjecture with multiple invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabian Gundlach","submitted_at":"2022-11-30T02:39:53Z","abstract_excerpt":"We define invariants $\\operatorname{inv}_1,\\dots,\\operatorname{inv}_m$ of Galois extensions of number fields with a fixed Galois group. Then, we propose a heuristic in the spirit of Malle's conjecture which asymptotically predicts the number of extensions that satisfy $\\operatorname{inv}_i\\leq X_i$ for all $X_i$. The resulting conjecture is proved for abelian Galois groups. We also describe refined Artin conductors that carry essentially the same information as the invariants $\\operatorname{inv}_1,\\dots,\\operatorname{inv}_m$."},"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":"2211.16698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-11-30T02:39:53Z","cross_cats_sorted":[],"title_canon_sha256":"96d47c3ee6b88629053d243a741a6ca2e308cc8c4fda69e4123eab7b769822f3","abstract_canon_sha256":"420711c1ffe7181a7b12c4bd373892363e742a2b3293d55aaa0774b3a6ff5dac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:21:09.895472Z","signature_b64":"Gf3wmPca+p/hg+9c6kPDjfGt8Bhbbchttbol+KGyCRMlW/8bjXCvJiU58gHZev4JjoWumXjeQIJbCZL+tnXYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49de9be8c3c0119a539d7c8be53cde7a255851ba4ec0ddb2554fe3b31fdc407d","last_reissued_at":"2026-07-05T05:21:09.894981Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:21:09.894981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Malle's conjecture with multiple invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabian Gundlach","submitted_at":"2022-11-30T02:39:53Z","abstract_excerpt":"We define invariants $\\operatorname{inv}_1,\\dots,\\operatorname{inv}_m$ of Galois extensions of number fields with a fixed Galois group. Then, we propose a heuristic in the spirit of Malle's conjecture which asymptotically predicts the number of extensions that satisfy $\\operatorname{inv}_i\\leq X_i$ for all $X_i$. The resulting conjecture is proved for abelian Galois groups. We also describe refined Artin conductors that carry essentially the same information as the invariants $\\operatorname{inv}_1,\\dots,\\operatorname{inv}_m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.16698","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/2211.16698/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":"2211.16698","created_at":"2026-07-05T05:21:09.895038+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.16698v1","created_at":"2026-07-05T05:21:09.895038+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.16698","created_at":"2026-07-05T05:21:09.895038+00:00"},{"alias_kind":"pith_short_12","alias_value":"JHPJX2GDYAIZ","created_at":"2026-07-05T05:21:09.895038+00:00"},{"alias_kind":"pith_short_16","alias_value":"JHPJX2GDYAIZUU45","created_at":"2026-07-05T05:21:09.895038+00:00"},{"alias_kind":"pith_short_8","alias_value":"JHPJX2GD","created_at":"2026-07-05T05:21:09.895038+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.04983","citing_title":"The leading constant in Malle's conjecture","ref_index":39,"is_internal_anchor":false},{"citing_arxiv_id":"2602.23619","citing_title":"Counting number fields using multiple Dirichlet series","ref_index":12,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI","json":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI.json","graph_json":"https://pith.science/api/pith-number/JHPJX2GDYAIZUU45PSF6KPG6PI/graph.json","events_json":"https://pith.science/api/pith-number/JHPJX2GDYAIZUU45PSF6KPG6PI/events.json","paper":"https://pith.science/paper/JHPJX2GD"},"agent_actions":{"view_html":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI","download_json":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI.json","view_paper":"https://pith.science/paper/JHPJX2GD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.16698&json=true","fetch_graph":"https://pith.science/api/pith-number/JHPJX2GDYAIZUU45PSF6KPG6PI/graph.json","fetch_events":"https://pith.science/api/pith-number/JHPJX2GDYAIZUU45PSF6KPG6PI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI/action/storage_attestation","attest_author":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI/action/author_attestation","sign_citation":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI/action/citation_signature","submit_replication":"https://pith.science/pith/JHPJX2GDYAIZUU45PSF6KPG6PI/action/replication_record"}},"created_at":"2026-07-05T05:21:09.895038+00:00","updated_at":"2026-07-05T05:21:09.895038+00:00"}