{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:IH4MYGX5DDFNTDZY3IUWILAEOC","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":"5ecc2410ed333e4f5268c44b11b278c18885fa2d09482dcd7ffb82271f8acc10","cross_cats_sorted":["hep-th","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-12-07T22:04:10Z","title_canon_sha256":"a3473a3a418179fd7548fdc5e5f0785420602235228628d14922233404de18e2"},"schema_version":"1.0","source":{"id":"2012.04084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.04084","created_at":"2026-07-05T06:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"2012.04084v1","created_at":"2026-07-05T06:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.04084","created_at":"2026-07-05T06:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"IH4MYGX5DDFN","created_at":"2026-07-05T06:30:23Z"},{"alias_kind":"pith_short_16","alias_value":"IH4MYGX5DDFNTDZY","created_at":"2026-07-05T06:30:23Z"},{"alias_kind":"pith_short_8","alias_value":"IH4MYGX5","created_at":"2026-07-05T06:30:23Z"}],"graph_snapshots":[{"event_id":"sha256:c0f6bb9643953b59af24aa4eda3770ba02dd821265c2b642505f6e675b15f1cf","target":"graph","created_at":"2026-07-05T06:30:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2012.04084/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that standard machine-learning algorithms may be trained to predict certain invariants of low genus arithmetic curves. Using datasets of size around one hundred thousand, we demonstrate the utility of machine-learning in classification problems pertaining to the BSD invariants of an elliptic curve (including its rank and torsion subgroup), and the analogous invariants of a genus 2 curve. Our results show that a trained machine can efficiently classify curves according to these invariants with high accuracies (>0.97). For problems such as distinguishing between torsion orders, and the r","authors_text":"Kyu-Hwan Lee, Thomas Oliver, Yang-Hui He","cross_cats":["hep-th","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-12-07T22:04:10Z","title":"Machine-Learning Arithmetic Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.04084","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:f7c0b4aa6fa1f96dcfbf419189128874a3319ff7b852a411b5388ac04e3be5f2","target":"record","created_at":"2026-07-05T06:30:23Z","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":"5ecc2410ed333e4f5268c44b11b278c18885fa2d09482dcd7ffb82271f8acc10","cross_cats_sorted":["hep-th","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-12-07T22:04:10Z","title_canon_sha256":"a3473a3a418179fd7548fdc5e5f0785420602235228628d14922233404de18e2"},"schema_version":"1.0","source":{"id":"2012.04084","kind":"arxiv","version":1}},"canonical_sha256":"41f8cc1afd18cad98f38da29642c047081462abc95485ddcc3f24dcb6b7591df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41f8cc1afd18cad98f38da29642c047081462abc95485ddcc3f24dcb6b7591df","first_computed_at":"2026-07-05T06:30:23.133864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:30:23.133864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VrmEullvGfAjWOss4VS/7Q09ntYWPdPsJV6Rarxv5ULlahMTvD4AsWYfPDcBt8AQ1uy+3UDCZ9wLfIv9e2yJAg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:30:23.134299Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.04084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7c0b4aa6fa1f96dcfbf419189128874a3319ff7b852a411b5388ac04e3be5f2","sha256:c0f6bb9643953b59af24aa4eda3770ba02dd821265c2b642505f6e675b15f1cf"],"state_sha256":"d046e1c1cc01c4969193df13fcc58298de4acd0746c80bbf3befffbf91af8b36"}