{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7Q7TFUK7TN22GHCK2WLMB566NQ","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":"73d6f58ceafe5a3b2d824896ccb19e09cf9b5d8271bfb1c357a1a39a9ad7e395","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-23T00:03:20Z","title_canon_sha256":"cfc0ba64beea0afcfb474e5e4b803f0429c78b9daee1f6e9d383f5678ee40df8"},"schema_version":"1.0","source":{"id":"1412.7217","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7217","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7217v2","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7217","created_at":"2026-05-18T01:04:09Z"},{"alias_kind":"pith_short_12","alias_value":"7Q7TFUK7TN22","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7Q7TFUK7TN22GHCK","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7Q7TFUK7","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:70ee9f0f2f6e702f6079e65c0b6465c2c4967af5d60832974c5f8b795ae3bf2c","target":"graph","created_at":"2026-05-18T01:04:09Z","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 previous work of ours to all curves for which a good lift to characteristic zero is known. We develop all the necessary bounds, analyse the complexity of the algorithm and provide a complete 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":"2014-12-23T00:03:20Z","title":"Counting points on curves using a map to P^1, II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7217","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":"sha256:9af815f220e75940998a3381b5b88303ffeb54909e841ab66da4e49e1fabf917","target":"record","created_at":"2026-05-18T01:04:09Z","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":"73d6f58ceafe5a3b2d824896ccb19e09cf9b5d8271bfb1c357a1a39a9ad7e395","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-23T00:03:20Z","title_canon_sha256":"cfc0ba64beea0afcfb474e5e4b803f0429c78b9daee1f6e9d383f5678ee40df8"},"schema_version":"1.0","source":{"id":"1412.7217","kind":"arxiv","version":2}},"canonical_sha256":"fc3f32d15f9b75a31c4ad596c0f7de6c20fff7e3a4948b288600b8e7a25199ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc3f32d15f9b75a31c4ad596c0f7de6c20fff7e3a4948b288600b8e7a25199ee","first_computed_at":"2026-05-18T01:04:09.549541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:09.549541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JQ4J+cqOj5rLm3dT+P9AG5q5EP8ulA+URMJdVMqxpqpSorfXEGCoW35f7dWV4xSy8q8Qhl4Teh7vitUNsLMOCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:09.550543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7217","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9af815f220e75940998a3381b5b88303ffeb54909e841ab66da4e49e1fabf917","sha256:70ee9f0f2f6e702f6079e65c0b6465c2c4967af5d60832974c5f8b795ae3bf2c"],"state_sha256":"3e2d8cde016e94753305b88ff0d6cc3955145935ffbf166a4da746df7157c428"}