{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NLCG2KYBOX3JOXHLG5SAR3RS5I","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":"968daa6e836c7bec102c4b57da4e43e23ee62238af66863320940e03ae8027de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-13T13:04:55Z","title_canon_sha256":"f244ba7d38601b1f7e526925afb51e71c1f95cff70fc93f4aa88cce2a89bfc80"},"schema_version":"1.0","source":{"id":"1612.04137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04137","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04137v1","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04137","created_at":"2026-05-18T00:55:05Z"},{"alias_kind":"pith_short_12","alias_value":"NLCG2KYBOX3J","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NLCG2KYBOX3JOXHL","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NLCG2KYB","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:d303a5db678b890d32559d280c3172d67a639f2565bf684541a7026bd94d5e62","target":"graph","created_at":"2026-05-18T00:55:05Z","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":"The distribution of the number of points on abelian covers of $\\mathbb{P}1(\\mathbb{F}_q)$ ranging over an irreducible moduli space has been answered in recent work by the author. Bucur, et al. determined the distribution over the whole moduli space for curves with Gal$(K(C)/K)$ a prime cyclic. In this paper, we prove a result towards determining the distribution over the whole moduli space of curves with Gal$(K(C)/K)$ any abelian group. We successfully determine the distribution in the case Gal$(K(C)/K)$ is a power of a prime cyclic.","authors_text":"Patrick Meisner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-13T13:04:55Z","title":"Number of Points on the Full Moduli Space of Curves over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04137","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":"sha256:949e3684e0cdfd1903862df6dd00e404f03936a063948240d12b0eaa28e5a968","target":"record","created_at":"2026-05-18T00:55:05Z","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":"968daa6e836c7bec102c4b57da4e43e23ee62238af66863320940e03ae8027de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-13T13:04:55Z","title_canon_sha256":"f244ba7d38601b1f7e526925afb51e71c1f95cff70fc93f4aa88cce2a89bfc80"},"schema_version":"1.0","source":{"id":"1612.04137","kind":"arxiv","version":1}},"canonical_sha256":"6ac46d2b0175f6975ceb376408ee32ea3163bfbc974a46f4a620d27755f5b58e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ac46d2b0175f6975ceb376408ee32ea3163bfbc974a46f4a620d27755f5b58e","first_computed_at":"2026-05-18T00:55:05.388773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:05.388773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m3sSonxzRCH/DWirjBX8qNjY515Vz0jLvpTiTaEZAWNQ8w/DeShu1pICyRF5/8jgK6RqwMurS8GLHgWiGLnsBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:05.389419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:949e3684e0cdfd1903862df6dd00e404f03936a063948240d12b0eaa28e5a968","sha256:d303a5db678b890d32559d280c3172d67a639f2565bf684541a7026bd94d5e62"],"state_sha256":"4753ec04e0fe2a1591314224a20e66ece3fecf7e991d874989602802e902cd51"}