{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PNKU5QWI6HTCV2JAFPYZKD5YSF","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":"465c3ce2592a3b0f101bcc64602695a86b3d419eb5c20f80fe3052360040ec7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-10T17:15:25Z","title_canon_sha256":"75891e5f693109146a333e18fb0a7d6478a53682374509a76960bd65a7d06d6e"},"schema_version":"1.0","source":{"id":"1509.03234","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03234","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03234v1","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03234","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"PNKU5QWI6HTC","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PNKU5QWI6HTCV2JA","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PNKU5QWI","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:dd46b002f881a0fb9becdb738578db6f39d6072b3f77ca4af2631041f0359e74","target":"graph","created_at":"2026-05-18T01:33:24Z","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":"Let $E$ be an elliptic curve over a number field $K$. Descent calculations on $E$ can be used to find upper bounds for the rank of the Mordell-Weil group, and to compute covering curves that assist in the search for generators of this group. The general method of 4-descent, developed in the PhD theses of Siksek, Womack and Stamminger, has been implemented in Magma (when $K={\\mathbb Q}$) and works well for elliptic curves with sufficiently small discriminant. By extending work of Bremner and Cassels, we describe the improvements that can be made when $E$ has a rational 2-torsion point. In parti","authors_text":"Tom Fisher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-10T17:15:25Z","title":"Higher descents on an elliptic curve with a rational 2-torsion point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03234","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:cf8882aac025ad1a7c1555e444165901e958bb935f09803fa1c0c5d7cfd4e962","target":"record","created_at":"2026-05-18T01:33:24Z","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":"465c3ce2592a3b0f101bcc64602695a86b3d419eb5c20f80fe3052360040ec7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-10T17:15:25Z","title_canon_sha256":"75891e5f693109146a333e18fb0a7d6478a53682374509a76960bd65a7d06d6e"},"schema_version":"1.0","source":{"id":"1509.03234","kind":"arxiv","version":1}},"canonical_sha256":"7b554ec2c8f1e62ae9202bf1950fb8917e63fe0cf1ef4af119a1c49d76e40464","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b554ec2c8f1e62ae9202bf1950fb8917e63fe0cf1ef4af119a1c49d76e40464","first_computed_at":"2026-05-18T01:33:24.974126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:24.974126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vjnu6yuoVqcBBUPtumRSLsb/9mkkDMNQ2ftnkQbcy0vSNYYHY5bqXKfWtRoR8RMctNxkkR26zW4rlplN4fe0Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:24.974679Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03234","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf8882aac025ad1a7c1555e444165901e958bb935f09803fa1c0c5d7cfd4e962","sha256:dd46b002f881a0fb9becdb738578db6f39d6072b3f77ca4af2631041f0359e74"],"state_sha256":"f3dc928d5f634fcda90f2ef389161623b245fa52331a39e3f1c96a7f525eb130"}