{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6ZSBIA6ELJ7I5TRHIPPRH5BOCV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2904650d7729c43568d4e3d30c6ddb73ccf9881cc8063509a7020d5033de94b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-22T22:35:26Z","title_canon_sha256":"1eb78238d59967e7278937bef9ccfa0b7e68daa1230f898b3a72fa0e91f609ba"},"schema_version":"1.0","source":{"id":"1302.5728","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5728","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5728v1","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5728","created_at":"2026-05-18T03:32:44Z"},{"alias_kind":"pith_short_12","alias_value":"6ZSBIA6ELJ7I","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6ZSBIA6ELJ7I5TRH","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6ZSBIA6E","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:cec4bc835070345d5b647f32753366aaccdb964b0a5692ef1470549d3ec03fe2","target":"graph","created_at":"2026-05-18T03:32:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $k$ be a cubic field. We give an explicit formula for the Dirichlet series $\\sum_K|\\Disc(K)|^{-s}$, where the sum is over isomorphism classes of all quartic fields whose cubic resolvent field is isomorphic to $k$. Our work is a sequel to an unpublished preprint of Cohen, Diaz y Diaz, and Olivier, and we include complete proofs of their results so as not to rely on unpublished work.\n  This is a companion to a previous paper where we compute the Dirichlet series associated to cubic fields having a given quadratic resolvent.","authors_text":"Frank Thorne, Henri Cohen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-22T22:35:26Z","title":"Dirichlet series associated to quartic fields with given resolvent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5728","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1aa7baf7afa1b12837fa239f2bd015dd0e5c7c82c0f6a5447f3a105d3c1562f7","target":"record","created_at":"2026-05-18T03:32:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2904650d7729c43568d4e3d30c6ddb73ccf9881cc8063509a7020d5033de94b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-22T22:35:26Z","title_canon_sha256":"1eb78238d59967e7278937bef9ccfa0b7e68daa1230f898b3a72fa0e91f609ba"},"schema_version":"1.0","source":{"id":"1302.5728","kind":"arxiv","version":1}},"canonical_sha256":"f6641403c45a7e8ece2743df13f42e15638c1bcb447620f669e84b66f0a3dbbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6641403c45a7e8ece2743df13f42e15638c1bcb447620f669e84b66f0a3dbbe","first_computed_at":"2026-05-18T03:32:44.075891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:44.075891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ALGyslLo05Sfzl6jV2BbhqqEv4pR8JizkiETXc7Q9atOQMaUesAOm+ZR28nb8plz7HOghlYbzZT05o6jeyxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:44.076663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5728","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1aa7baf7afa1b12837fa239f2bd015dd0e5c7c82c0f6a5447f3a105d3c1562f7","sha256:cec4bc835070345d5b647f32753366aaccdb964b0a5692ef1470549d3ec03fe2"],"state_sha256":"bcfe6dbee8a4420df4fc7c32b9a97123fd08c0bd7c736dd1840ac39ea395ae91"}