{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ILTCHWVRRHILJGTOVCD5YBQYDK","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":"2e2918546b4c1539e512eeea81a767b4456b0e55a044ecf96f6c2f01d357692b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-03-21T15:31:37Z","title_canon_sha256":"68dd18866b8b9b81655d4a0984141a72af9bce8268bdd9bb527c71569ad3e114"},"schema_version":"1.0","source":{"id":"2503.17228","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.17228","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"arxiv_version","alias_value":"2503.17228v3","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.17228","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"pith_short_12","alias_value":"ILTCHWVRRHIL","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"pith_short_16","alias_value":"ILTCHWVRRHILJGTO","created_at":"2026-07-05T11:28:15Z"},{"alias_kind":"pith_short_8","alias_value":"ILTCHWVR","created_at":"2026-07-05T11:28:15Z"}],"graph_snapshots":[{"event_id":"sha256:aa1aeb1f9f22da510ccf02dbcb54abbe62bbb7cfddea47a5ad53140148f7ec4d","target":"graph","created_at":"2026-07-05T11:28:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.17228/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the mean value of the first moment of primitive cubic $L$-functions over $\\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum\n  \\begin{equation*}\n  \\sum_{\\substack{\\chi\\ primitive\\ cubic\\\\ genus(\\chi)=g}}L_q(\\frac{1}{2}, \\chi),\n  \\end{equation*} where $L_q(s,\\chi)$ denotes the $L$-function associated with primitive cubic character $\\chi$. Using double Dirichlet series, we derive an error term of size $q^{(\\frac{7}{8}+\\varepsilon)g}$.","authors_text":"Zhongqiu Fang, Ziwei Hong","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-03-21T15:31:37Z","title":"Mean value of cubic $L$-funcitons with fixed genus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.17228","kind":"arxiv","version":3},"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:a64a808f0d86b8bc4454884660c24fe48ece2ecf55089b7d1d3db9c0886fce19","target":"record","created_at":"2026-07-05T11:28:15Z","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":"2e2918546b4c1539e512eeea81a767b4456b0e55a044ecf96f6c2f01d357692b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-03-21T15:31:37Z","title_canon_sha256":"68dd18866b8b9b81655d4a0984141a72af9bce8268bdd9bb527c71569ad3e114"},"schema_version":"1.0","source":{"id":"2503.17228","kind":"arxiv","version":3}},"canonical_sha256":"42e623dab189d0b49a6ea887dc06181a8f93fd12f237ff8bdfe279c0c1233ac6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42e623dab189d0b49a6ea887dc06181a8f93fd12f237ff8bdfe279c0c1233ac6","first_computed_at":"2026-07-05T11:28:15.232573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:28:15.232573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KlfkMvjGrHnpeXuO9rCXkM81egWvwACgT8bDhRo2UAZGCMSaOC8/nMDk5fG8h5Nz5vS0og2J1HHxBgDbC/MvBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:28:15.233011Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.17228","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a64a808f0d86b8bc4454884660c24fe48ece2ecf55089b7d1d3db9c0886fce19","sha256:aa1aeb1f9f22da510ccf02dbcb54abbe62bbb7cfddea47a5ad53140148f7ec4d"],"state_sha256":"777d26a09eacde84aada5eb7f284f9d09ced3d8ac923a6ea13b514ea8e57f9ed"}