{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VM6XL36XFRXWXS7LF4MJUDLMJQ","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":"03d0caadfa3d963add505d4d5895de7f37ff081f2a818d93df81d6416d18b268","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-08T13:40:04Z","title_canon_sha256":"e6879798d766a47be48b3fe11742cb7adf82c421e6d79b0358d719614143d1c0"},"schema_version":"1.0","source":{"id":"1808.02887","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02887","created_at":"2026-07-05T00:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02887v2","created_at":"2026-07-05T00:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02887","created_at":"2026-07-05T00:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"VM6XL36XFRXW","created_at":"2026-07-05T00:16:02Z"},{"alias_kind":"pith_short_16","alias_value":"VM6XL36XFRXWXS7L","created_at":"2026-07-05T00:16:02Z"},{"alias_kind":"pith_short_8","alias_value":"VM6XL36X","created_at":"2026-07-05T00:16:02Z"}],"graph_snapshots":[{"event_id":"sha256:f801a8ebcfe848b90976616624870b9b17f2ff150361eb209fc6835c376be40f","target":"graph","created_at":"2026-07-05T00:16:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1808.02887/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given an elliptic curve $E/\\mathbb{Q}$ with torsion subgroup $G = E(\\mathbb{Q})_{\\rm tors}$ we study what groups (up to isomorphism) can occur as the torsion subgroup of $E$ base-extended to $K$, a degree 6 extension of $\\mathbb{Q}$. We also determine which groups $H = E(K)_{\\rm tors}$ can occur infinitely often and which ones occur for only finitely many curves. This article is a first step towards a complete classification of torsion growth of over sextic fields.","authors_text":"Enrique Gonz\\'alez-Jim\\'enez, Harris B. Daniels","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-08T13:40:04Z","title":"On the torsion of rational elliptic curves over sextic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02887","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":"sha256:264afe6332778e1e5ae1088794e6abfa66fa9f22a7ded20cb98ee104b9899b3d","target":"record","created_at":"2026-07-05T00:16:02Z","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":"03d0caadfa3d963add505d4d5895de7f37ff081f2a818d93df81d6416d18b268","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-08-08T13:40:04Z","title_canon_sha256":"e6879798d766a47be48b3fe11742cb7adf82c421e6d79b0358d719614143d1c0"},"schema_version":"1.0","source":{"id":"1808.02887","kind":"arxiv","version":2}},"canonical_sha256":"ab3d75efd72c6f6bcbeb2f189a0d6c4c2d3ea6570525601ad854c4bff2ea6d26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab3d75efd72c6f6bcbeb2f189a0d6c4c2d3ea6570525601ad854c4bff2ea6d26","first_computed_at":"2026-07-05T00:16:02.327551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:16:02.327551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vo+BRWlPgKxMR4FownYSWY+X/Pm/I7kepGfLJ2AwOSC24wlq9XGYaVxuRc8KCnRD7TiYYtHd5i8eY8ctJfxaCg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:16:02.327907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02887","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:264afe6332778e1e5ae1088794e6abfa66fa9f22a7ded20cb98ee104b9899b3d","sha256:f801a8ebcfe848b90976616624870b9b17f2ff150361eb209fc6835c376be40f"],"state_sha256":"74d0d50cd75309a64ef3e32a988ecf6dc94b65b3aca6c52a5d53ef8babb0371f"}