{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RL6IVO7HBZWJ3XRYEJ76RSN544","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":"c9bb93195a2a91b9a1e6f75d000a2b4566d95734061140fac7ffe6baa880e489","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-30T02:26:48Z","title_canon_sha256":"463e581bbea93eb8804e939636affba2a7e793a3cb8aa4b68de2e935fac9963c"},"schema_version":"1.0","source":{"id":"1301.7124","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7124","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7124v1","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7124","created_at":"2026-05-18T03:35:01Z"},{"alias_kind":"pith_short_12","alias_value":"RL6IVO7HBZWJ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RL6IVO7HBZWJ3XRY","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RL6IVO7H","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:3171ddbdc4c68d3bfc94f8d5c15ddee36adf940e175b3b5b815f57c318ad3709","target":"graph","created_at":"2026-05-18T03:35:01Z","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":"For a function field $k$ over a finite field with $\\mathbb{F}_q$ as the field of constant, and a finite abelian group $G$ whose exponent is divisible by $q-1$, we study the distribution of zeta zeroes for a random $G$-extension of $k$, ordered by the degree of conductors. We prove that when the degree goes to infinity, the number of zeta zeroes lying in a prescribed arc is uniformly distributed and the variance follows a Gaussian distribution.","authors_text":"Maosheng Xiong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-30T02:26:48Z","title":"Distribution of zeta zeroes for abelian covers of algebraic curves over a finite field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7124","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":"sha256:597c9908da7db41267dfa20244cf8fd5e275cf84db7fb96b1cd75abcf72de7e2","target":"record","created_at":"2026-05-18T03:35:01Z","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":"c9bb93195a2a91b9a1e6f75d000a2b4566d95734061140fac7ffe6baa880e489","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-30T02:26:48Z","title_canon_sha256":"463e581bbea93eb8804e939636affba2a7e793a3cb8aa4b68de2e935fac9963c"},"schema_version":"1.0","source":{"id":"1301.7124","kind":"arxiv","version":1}},"canonical_sha256":"8afc8abbe70e6c9dde38227fe8c9bde738b69c9b7e435c2ca1e7be278f8d194a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8afc8abbe70e6c9dde38227fe8c9bde738b69c9b7e435c2ca1e7be278f8d194a","first_computed_at":"2026-05-18T03:35:01.231557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:01.231557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mYdfXrWfQGaNTqwvAXkBMJz7t5+jPSVLgT2Zo4zTzUlQ7VC4fnlwympYkPFRYw4CjtuJwOUOpXgUlakxVC4LAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:01.232365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.7124","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:597c9908da7db41267dfa20244cf8fd5e275cf84db7fb96b1cd75abcf72de7e2","sha256:3171ddbdc4c68d3bfc94f8d5c15ddee36adf940e175b3b5b815f57c318ad3709"],"state_sha256":"f9829265f3fbe63ed40d6c8cdb26b2566f0185c96d425de8eb65cb42a5b77a9f"}