{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:W44SH4E4BKMGZD2MM7BR3OXST7","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":"23dc8d0f43048df97734b5a41a32bf8c1ababc548d1801cc79a5843ebe78174b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-14T02:46:39Z","title_canon_sha256":"db6ea7874007f084739821fbc8f3ccf197deb6df57e3e5dbd40281be9b6b685e"},"schema_version":"1.0","source":{"id":"2605.14288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.14288","created_at":"2026-05-17T23:39:10Z"},{"alias_kind":"arxiv_version","alias_value":"2605.14288v1","created_at":"2026-05-17T23:39:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14288","created_at":"2026-05-17T23:39:10Z"},{"alias_kind":"pith_short_12","alias_value":"W44SH4E4BKMG","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"W44SH4E4BKMGZD2M","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"W44SH4E4","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:eb11b66839c035e7069b505bd02eb275e2b227458326aecce1b51a62f32f9815","target":"graph","created_at":"2026-05-17T23:39:10Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We demonstrate that the underlying datasets contain significant redundancy within quadratic twist classes, which alone is sufficient to produce highly accurate predictions."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the performance drop on the new unique-twist-class dataset is caused by removal of redundancy rather than by changes in data distribution or model capacity."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Redundancy within quadratic twist classes in elliptic curve datasets is sufficient to produce highly accurate machine learning predictions of Frobenius traces."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Redundancy within quadratic twist classes of elliptic curves suffices for highly accurate machine learning predictions of their Frobenius traces."}],"snapshot_sha256":"4c70238ab09b8e88e341a00b3661202bf6ae70751db30f7a186b234d7c423aea"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"dd90934149a70e59e29e9275f7ef0f60cea4911eb40cf8d0a9008842b79bc9ff"},"paper":{"abstract_excerpt":"Recent interest in applying machine learning methods to predict invariants of mathematical objects has yielded models with surprisingly strong performance, including those predicting traces of Frobenius for elliptic curves. We demonstrate that the underlying datasets contain significant redundancy within quadratic twist classes, which alone is sufficient to produce highly accurate predictions. To ensure future models capture new arithmetic properties rather than potentially exploiting these dataset artifacts, we introduce a benchmark dataset consisting exclusively of unique twist class represe","authors_text":"Angelica Babei, Malick Kebe, Ujjawal Shah","cross_cats":[],"headline":"Redundancy within quadratic twist classes of elliptic curves suffices for highly accurate machine learning predictions of their Frobenius traces.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-14T02:46:39Z","title":"How Twist Class Redundancy Drives the Prediction of Traces of Frobenius of Elliptic Curves"},"references":{"count":27,"internal_anchors":0,"resolved_work":27,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"M. Amir, Y.-H. He, K.-H. Lee, T. Oliver, and E. Sultanow. Machine learning class numbers of real quadratic fields.https://arxiv.org/pdf/2209.09283, 2022. arXiv:math.NT:2209.09283","work_id":"d1d40afb-287f-471e-8e33-ddbdb20c63fa","year":2022},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Frobenius traces for a set of (quadratic) twist classes of elliptic curves of conductor up to 10 7, May 2026","work_id":"5ba29c31-b1f6-4b60-80e2-528ebd9dfcad","year":2026},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Banwait, AJ Fing, Xiaoyu Huang, and Deependra Singh","work_id":"9be8f057-d34a-4ddd-8e80-3dfc4131801e","year":2025},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Learning euler factors of elliptic curves.Advances in Theoretical and Math- ematical Physics, 29(8):2327–2351, 2025","work_id":"390fcbdd-5bba-4ae6-9991-4a4848584136","year":2025},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Booker, Min Lee, and David Lowry-Duda","work_id":"93cafc15-3dad-4eee-8064-5eed9347491e","year":2023}],"snapshot_sha256":"bbf4959ec00a546853966e861fe07fb8e4252bef960cbce4cb07e350bd485ba9"},"source":{"id":"2605.14288","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-15T02:39:05.373601Z","id":"fbe0f108-2957-4588-bdab-23012493731d","model_set":{"reader":"grok-4.3"},"one_line_summary":"Redundancy within quadratic twist classes in elliptic curve datasets is sufficient to produce highly accurate machine learning predictions of Frobenius traces.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Redundancy within quadratic twist classes of elliptic curves suffices for highly accurate machine learning predictions of their Frobenius traces.","strongest_claim":"We demonstrate that the underlying datasets contain significant redundancy within quadratic twist classes, which alone is sufficient to produce highly accurate predictions.","weakest_assumption":"That the performance drop on the new unique-twist-class dataset is caused by removal of redundancy rather than by changes in data distribution or model capacity."}},"verdict_id":"fbe0f108-2957-4588-bdab-23012493731d"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d5c27b9ee90166d72674277b6d82969483b2d1da01cddd3c591e24afc21dc6a7","target":"record","created_at":"2026-05-17T23:39:10Z","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":"23dc8d0f43048df97734b5a41a32bf8c1ababc548d1801cc79a5843ebe78174b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-14T02:46:39Z","title_canon_sha256":"db6ea7874007f084739821fbc8f3ccf197deb6df57e3e5dbd40281be9b6b685e"},"schema_version":"1.0","source":{"id":"2605.14288","kind":"arxiv","version":1}},"canonical_sha256":"b73923f09c0a986c8f4c67c31dbaf29fea10a198baf7c94b8bd39b7260976007","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b73923f09c0a986c8f4c67c31dbaf29fea10a198baf7c94b8bd39b7260976007","first_computed_at":"2026-05-17T23:39:10.222818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:10.222818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UO2ololbz/KHRLtoShaXiXSHdBgY/atosmf4pnXtCmSLSHnpWQNetnvSB43JGkNjP1iXx8fjxwrfJvdKNbmtAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:10.223303Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.14288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5c27b9ee90166d72674277b6d82969483b2d1da01cddd3c591e24afc21dc6a7","sha256:eb11b66839c035e7069b505bd02eb275e2b227458326aecce1b51a62f32f9815"],"state_sha256":"67eb16f1fd3cdaeb8dc990b0253edc0f7d398d1e6338c4c54d8d967f43e234ec"}