{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:MGDAK4OUHSGDZBNVMO7IXXGJNC","short_pith_number":"pith:MGDAK4OU","schema_version":"1.0","canonical_sha256":"61860571d43c8c3c85b563be8bdcc968ac1a375c0982365f6dfb0f3d57497461","source":{"kind":"arxiv","id":"2405.08383","version":1},"attestation_state":"computed","paper":{"title":"Faithful Artin induction and the Chebotarev density theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.NT","authors_text":"Alexander Smith, Robert J. Lemke Oliver","submitted_at":"2024-05-14T07:30:11Z","abstract_excerpt":"Given a finite group G, we prove that the vector space spanned by the faithful irreducible characters of G is generated by the monomial characters in the vector space. As a consequence, we show that in any family of G-extensions of a fixed number field F, almost all are subject to a strong effective version of the Chebotarev density theorem. We use this version of the Chebotarev density theorem to deduce several consequences for class groups in families of number fields."},"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":"2405.08383","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-05-14T07:30:11Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"05f70a7065eb6df7136bae7909ad439f8c102b866d27c243fcccdfc7f22d3417","abstract_canon_sha256":"70a468e5bcd67f38bb3f0077a1109af186d1c6b88ecfdb54f5fc16a8b44dd5c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:18:59.711984Z","signature_b64":"cuYLXXxRo3xYwyb5DZeMakIX03Tcn6q/de/0IiAMHw3tNPcY5s5Ye5JM4G+Dj31GaD0PLwxFzwYwcZZjBeY0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61860571d43c8c3c85b563be8bdcc968ac1a375c0982365f6dfb0f3d57497461","last_reissued_at":"2026-07-05T08:18:59.711513Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:18:59.711513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Faithful Artin induction and the Chebotarev density theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.NT","authors_text":"Alexander Smith, Robert J. Lemke Oliver","submitted_at":"2024-05-14T07:30:11Z","abstract_excerpt":"Given a finite group G, we prove that the vector space spanned by the faithful irreducible characters of G is generated by the monomial characters in the vector space. As a consequence, we show that in any family of G-extensions of a fixed number field F, almost all are subject to a strong effective version of the Chebotarev density theorem. We use this version of the Chebotarev density theorem to deduce several consequences for class groups in families of number fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.08383","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/2405.08383/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":"2405.08383","created_at":"2026-07-05T08:18:59.711570+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.08383v1","created_at":"2026-07-05T08:18:59.711570+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.08383","created_at":"2026-07-05T08:18:59.711570+00:00"},{"alias_kind":"pith_short_12","alias_value":"MGDAK4OUHSGD","created_at":"2026-07-05T08:18:59.711570+00:00"},{"alias_kind":"pith_short_16","alias_value":"MGDAK4OUHSGDZBNV","created_at":"2026-07-05T08:18:59.711570+00:00"},{"alias_kind":"pith_short_8","alias_value":"MGDAK4OU","created_at":"2026-07-05T08:18:59.711570+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.18574","citing_title":"Inductive methods for counting number fields","ref_index":1985,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MGDAK4OUHSGDZBNVMO7IXXGJNC","json":"https://pith.science/pith/MGDAK4OUHSGDZBNVMO7IXXGJNC.json","graph_json":"https://pith.science/api/pith-number/MGDAK4OUHSGDZBNVMO7IXXGJNC/graph.json","events_json":"https://pith.science/api/pith-number/MGDAK4OUHSGDZBNVMO7IXXGJNC/events.json","paper":"https://pith.science/paper/MGDAK4OU"},"agent_actions":{"view_html":"https://pith.science/pith/MGDAK4OUHSGDZBNVMO7IXXGJNC","download_json":"https://pith.science/pith/MGDAK4OUHSGDZBNVMO7IXXGJNC.json","view_paper":"https://pith.science/paper/MGDAK4OU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.08383&json=true","fetch_graph":"https://pith.science/api/pith-number/MGDAK4OUHSGDZBNVMO7IXXGJNC/graph.json","fetch_events":"https://pith.science/api/pith-number/MGDAK4OUHSGDZBNVMO7IXXGJNC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MGDAK4OUHSGDZBNVMO7IXXGJNC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MGDAK4OUHSGDZBNVMO7IXXGJNC/action/storage_attestation","attest_author":"https://pith.science/pith/MGDAK4OUHSGDZBNVMO7IXXGJNC/action/author_attestation","sign_citation":"https://pith.science/pith/MGDAK4OUHSGDZBNVMO7IXXGJNC/action/citation_signature","submit_replication":"https://pith.science/pith/MGDAK4OUHSGDZBNVMO7IXXGJNC/action/replication_record"}},"created_at":"2026-07-05T08:18:59.711570+00:00","updated_at":"2026-07-05T08:18:59.711570+00:00"}