{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2PALJ2VSDAL6KAHHGR6PEYD6AQ","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":"161f533e05fc81ee549c4446730ea42b543bc7994a794af29f6f256a62d9cc9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-01T05:03:31Z","title_canon_sha256":"181209979f3140ad624b9b3fcb7ac0feee0208f3d637b11a0fa588cb02e9c58b"},"schema_version":"1.0","source":{"id":"1710.00294","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00294","created_at":"2026-05-18T00:29:28Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00294v2","created_at":"2026-05-18T00:29:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00294","created_at":"2026-05-18T00:29:28Z"},{"alias_kind":"pith_short_12","alias_value":"2PALJ2VSDAL6","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2PALJ2VSDAL6KAHH","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2PALJ2VS","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:a243cfddb0bb39646a1284db8321bc52c09a2f70f12dd098812ddf52470d1a47","target":"graph","created_at":"2026-05-18T00:29:28Z","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":"For certain elliptic curves $E/\\mathbb{Q}$ with $E(\\mathbb{Q})[2]=\\mathbb{Z}/2 \\mathbb{Z}$, we prove a criterion for prime twists of $E$ to have analytic rank 0 or 1, based on a mod 4 congruence of 2-adic logarithms of Heegner points. As an application, we prove new cases of Silverman's conjecture that there exists a positive proposition of prime twists of $E$ of rank zero (resp. positive rank).","authors_text":"Chao Li, Daniel Kriz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-01T05:03:31Z","title":"Prime twists of elliptic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00294","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":"sha256:2d4b982f1b5c579205cb3f223687a10c8894ed9956c64a18faf16c39fdb3aeff","target":"record","created_at":"2026-05-18T00:29:28Z","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":"161f533e05fc81ee549c4446730ea42b543bc7994a794af29f6f256a62d9cc9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-01T05:03:31Z","title_canon_sha256":"181209979f3140ad624b9b3fcb7ac0feee0208f3d637b11a0fa588cb02e9c58b"},"schema_version":"1.0","source":{"id":"1710.00294","kind":"arxiv","version":2}},"canonical_sha256":"d3c0b4eab21817e500e7347cf2607e04154ce7bedc2ecdad3d92eff62b1f55e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3c0b4eab21817e500e7347cf2607e04154ce7bedc2ecdad3d92eff62b1f55e7","first_computed_at":"2026-05-18T00:29:28.390611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:28.390611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4fqDZN4j6Qf8Y594Puk8iL62470zlx5AoW8jTtyLbJZm1l+e1hdggtmmCm/HTcPTWshclanW7lijABCi9gBRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:28.391118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00294","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d4b982f1b5c579205cb3f223687a10c8894ed9956c64a18faf16c39fdb3aeff","sha256:a243cfddb0bb39646a1284db8321bc52c09a2f70f12dd098812ddf52470d1a47"],"state_sha256":"442905e7acef763ac4e282fb279390dee8605712f103ab78ff8c15de6bad9966"}