{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4SQFOHD6DRFI6LCJKPSOHD7BUA","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":"ef14ec88f923f6ce3605c8ad961e8318ed6cf510727c08b55b3305d793b5bf77","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-23T16:01:47Z","title_canon_sha256":"c3dd71250d96da6549f55821c7cd72d2912335259f7360eadce97d8f04c7c018"},"schema_version":"1.0","source":{"id":"1202.5221","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5221","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5221v3","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5221","created_at":"2026-05-18T03:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"4SQFOHD6DRFI","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4SQFOHD6DRFI6LCJ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4SQFOHD6","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:0a0f668de46980eb196091ad3a800fc93c51269893c79037b824d1891c85d71a","target":"graph","created_at":"2026-05-18T03:19:23Z","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":"We study cyclic finite Galois extensions of the rational function field of the projective line P^{1}(F_q) over a finite field F_q with q elements defined by considering quotient curves by finite subgroups of the projective linear group PGL(2,q), and we enumerate them expressing the count in terms of Stirling numbers.","authors_text":"Alberto Besana, Cristina Martinez Ramirez","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-23T16:01:47Z","title":"Some remarks on cyclic Galois coverings of the projective line over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5221","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:c377517a0f9cf01b4aef96b5a68f9736dec62479dc1f64a7a37fe8f7810e7ad8","target":"record","created_at":"2026-05-18T03:19:23Z","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":"ef14ec88f923f6ce3605c8ad961e8318ed6cf510727c08b55b3305d793b5bf77","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-23T16:01:47Z","title_canon_sha256":"c3dd71250d96da6549f55821c7cd72d2912335259f7360eadce97d8f04c7c018"},"schema_version":"1.0","source":{"id":"1202.5221","kind":"arxiv","version":3}},"canonical_sha256":"e4a0571c7e1c4a8f2c4953e4e38fe1a00a651756249c3d86b4ab7ac8a2331471","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4a0571c7e1c4a8f2c4953e4e38fe1a00a651756249c3d86b4ab7ac8a2331471","first_computed_at":"2026-05-18T03:19:23.430064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:23.430064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"er3KWoy4a0tVFJ4fXU4GA3iT/C9HZjCKHKeIV0TnSlfyFo6y8jO4SfVq1sZpqsUkyk/jjEn7XsLHXTlw0n5cAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:23.430692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5221","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c377517a0f9cf01b4aef96b5a68f9736dec62479dc1f64a7a37fe8f7810e7ad8","sha256:0a0f668de46980eb196091ad3a800fc93c51269893c79037b824d1891c85d71a"],"state_sha256":"46f8971f2ef2aac20d9c4b60cd52f50b2aab3f73125c18cc7404806474ad0c3b"}