{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:T6VRM4PA4LEKABDM6CI5UPQP2U","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":"33bcc0672bb19a9a778ab02864d1c63bfc24884aaeb67ea9659a159a7f17f285","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-27T01:12:41Z","title_canon_sha256":"949b47f2cf9c2b64e20ea7757fb4780af389612d6ea367f5b38457dd18b640a7"},"schema_version":"1.0","source":{"id":"1402.6758","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6758","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6758v2","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6758","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"T6VRM4PA4LEK","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T6VRM4PA4LEKABDM","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T6VRM4PA","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:4c035a5b4f08b62e8322061132bae9b195345dfc3ed24f2a24d78f15bbeb5268","target":"graph","created_at":"2026-05-18T02:43:09Z","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 introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends Kedlaya's algorithm to a very general class of curves using a map to the projective line. We develop all the necessary bounds, analyse the complexity of the algorithm and provide some examples computed with our implementation.","authors_text":"Jan Tuitman","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-27T01:12:41Z","title":"Counting points on curves using a map to P^1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6758","kind":"arxiv","version":2},"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":"sha256:9b6bee3038e6ede0834b23df53e87f0cd3bce05089e9b715b2d0cfcbe74b21e1","target":"record","created_at":"2026-05-18T02:43:09Z","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":"33bcc0672bb19a9a778ab02864d1c63bfc24884aaeb67ea9659a159a7f17f285","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-27T01:12:41Z","title_canon_sha256":"949b47f2cf9c2b64e20ea7757fb4780af389612d6ea367f5b38457dd18b640a7"},"schema_version":"1.0","source":{"id":"1402.6758","kind":"arxiv","version":2}},"canonical_sha256":"9fab1671e0e2c8a0046cf091da3e0fd5117990e02217e1448082ce04fd014f0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fab1671e0e2c8a0046cf091da3e0fd5117990e02217e1448082ce04fd014f0e","first_computed_at":"2026-05-18T02:43:09.160986Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:09.160986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NSOMJ562Di1dWGz1u0ReY3U8PfhDqnmqIstE4BhcSj2nKUd/Z6dv8Xb4zaz85WFji1KbmteUp0pOv/6yPYipDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:09.161471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6758","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b6bee3038e6ede0834b23df53e87f0cd3bce05089e9b715b2d0cfcbe74b21e1","sha256:4c035a5b4f08b62e8322061132bae9b195345dfc3ed24f2a24d78f15bbeb5268"],"state_sha256":"4fa6fe1263c56c731737c24086649686d0e3b417bcf0b0311b3d1d9a943d7dc1"}