{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZSOIUZMLKZ4P6BBHOKRGIOMN3F","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":"f5e4aa36795b3f6571ccdcd350cba5f287a91a374e37b7a743463c931342e961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-02T00:10:16Z","title_canon_sha256":"05b753764d2042bf2d1058a2ad7382d859a3e2951f98f4ac0cc7bb114b0f550f"},"schema_version":"1.0","source":{"id":"1509.00528","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00528","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00528v5","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00528","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZSOIUZMLKZ4P","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZSOIUZMLKZ4P6BBH","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZSOIUZML","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:bf9bcb619ec0e7ac097a5b02bebac9355f5b7294b2f7c7b260465798a42a015a","target":"graph","created_at":"2026-05-18T00:25:06Z","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 $E/\\mathbb{Q}$ be an elliptic curve and let $\\mathbb{Q}(3^\\infty)$ be the compositum of all cubic extensions of $\\mathbb{Q}$. In this article we show that the torsion subgroup of $E(\\mathbb{Q}(3^\\infty))$ is finite and determine 20 possibilities for its structure, along with a complete description of the $\\overline{\\mathbb{Q}}$-isomorphism classes of elliptic curves that fall into each case. We provide rational parameterizations for each of the 16 torsion structures that occur for infinitely many $\\overline{\\mathbb{Q}}$-isomorphism classes of elliptic curves, and a complete list of $j$-inv","authors_text":"Alvaro Lozano-Robledo, Andrew V. Sutherland, Filip Najman, Harris B. Daniels","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-02T00:10:16Z","title":"Torsion subgroups of rational elliptic curves over the compositum of all cubic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00528","kind":"arxiv","version":5},"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:d24ad8a90dde2f74652ae03099a0f340a4ce779120263094e4ce7fe685b9ea8c","target":"record","created_at":"2026-05-18T00:25:06Z","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":"f5e4aa36795b3f6571ccdcd350cba5f287a91a374e37b7a743463c931342e961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-02T00:10:16Z","title_canon_sha256":"05b753764d2042bf2d1058a2ad7382d859a3e2951f98f4ac0cc7bb114b0f550f"},"schema_version":"1.0","source":{"id":"1509.00528","kind":"arxiv","version":5}},"canonical_sha256":"cc9c8a658b5678ff042772a264398dd94ee77f658c5040df552912332018eea8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc9c8a658b5678ff042772a264398dd94ee77f658c5040df552912332018eea8","first_computed_at":"2026-05-18T00:25:06.027765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:06.027765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hwBH+msb0mEx7c/wiYawAqgT1uqHvuhHgHx9BvOodr5ZtEqS1mGj2WPP6xV0cS0DID9eA17fGTWTnhakqIb+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:06.028198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00528","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d24ad8a90dde2f74652ae03099a0f340a4ce779120263094e4ce7fe685b9ea8c","sha256:bf9bcb619ec0e7ac097a5b02bebac9355f5b7294b2f7c7b260465798a42a015a"],"state_sha256":"6cfd37a98525b1387c842fcb723ff7d37dd281af6103463a8d09ccecda658883"}