{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XENFGUI3RWAPPWZWAU73I2LVVW","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":"4b908c8189092e2dc41a635bed15aefef085c8c39bf2330fc8f522ca98aa6463","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-21T03:50:17Z","title_canon_sha256":"47b32367f82e332cf5275ddc61fcde500033a7e24d1c69c5d6379fd2bca8bbfc"},"schema_version":"1.0","source":{"id":"1311.5306","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5306","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5306v1","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5306","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"XENFGUI3RWAP","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XENFGUI3RWAPPWZW","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XENFGUI3","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:d7656f2c54d100812f77b907fe93811e31a48b4070d9fb02a89df3dab6919be8","target":"graph","created_at":"2026-05-18T03:00:12Z","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":"A weaker form of a 1979 conjecture of Goldfeld states that for every elliptic curve $E/\\mathbb{Q}$, a positive proportion of its quadratic twists $E^{(d)}$ have rank 1. Using tools from Galois cohomology, we give criteria on E and d which force a positive proportion of the quadratic twists of E to have 3-Selmer rank 1 and global root number -1. We then give four nonisomorphic infinite families of elliptic curves $E_{m, n}$ which satisfy these criteria. Conditional on the rank part of the Birch and Swinnerton-Dyer conjecture, this verifies the aforementioned conjecture for infinitely many ellip","authors_text":"Zane Kun Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-21T03:50:17Z","title":"Quadratic Twists of Elliptic Curves with 3-Selmer Rank 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5306","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":"sha256:95828b2abca0dfb0f448525c10b50c7fe04582fc3667e0404f3cc564028a026f","target":"record","created_at":"2026-05-18T03:00:12Z","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":"4b908c8189092e2dc41a635bed15aefef085c8c39bf2330fc8f522ca98aa6463","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-21T03:50:17Z","title_canon_sha256":"47b32367f82e332cf5275ddc61fcde500033a7e24d1c69c5d6379fd2bca8bbfc"},"schema_version":"1.0","source":{"id":"1311.5306","kind":"arxiv","version":1}},"canonical_sha256":"b91a53511b8d80f7db36053fb46975ad824664f7caeb185de683b59ade101dd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b91a53511b8d80f7db36053fb46975ad824664f7caeb185de683b59ade101dd2","first_computed_at":"2026-05-18T03:00:12.196827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:12.196827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mq7LatLTtDtkKuhBnUtKI77vNK50DUQc/b/bjyIF7QAZcHjLZfactqCt4EnptPLiVnJHok9qHFhK/pHFPWdwDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:12.197659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.5306","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95828b2abca0dfb0f448525c10b50c7fe04582fc3667e0404f3cc564028a026f","sha256:d7656f2c54d100812f77b907fe93811e31a48b4070d9fb02a89df3dab6919be8"],"state_sha256":"f345b469d09f1810c067b4ec37ffd30541d0b7a53aa13a26b56ee7df970003ea"}