{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EN73V6PLFQWYV4UCOKUO3HRXTC","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":"684708d81efa587f5cb107f1e7a8569b99a2300733ac4e34359eaa541f6fad18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-11T13:34:22Z","title_canon_sha256":"d63c49365271034464b3876fe0ddd6ce357a158f0e7b3650f71f5b125403bcdd"},"schema_version":"1.0","source":{"id":"1403.2572","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2572","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2572v2","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2572","created_at":"2026-05-18T01:58:27Z"},{"alias_kind":"pith_short_12","alias_value":"EN73V6PLFQWY","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EN73V6PLFQWYV4UC","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EN73V6PL","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:e6f37fccab2583ffc1f0184cec75090e74040f014f3436589e70d15601e37371","target":"graph","created_at":"2026-05-18T01:58:27Z","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 K be a number field and let $\\mathcal{E}$ be an elliptic curve defined over $K$. Let $m$ be a positive integer. We denote by $K(\\mathcal{E}[m])$ the number fields obtained by adding to $K$ the coordinates of the $m$-torsion points of $\\mathcal{E}$. We look for small (sometimes \"minimal\") set of generators of $K(\\mathcal{E}[m])$. For $m=3$ and $m=4$, we describe explicit generators, degree and Galois groups of the extensions $K(\\mathcal{E}[m])/K$.","authors_text":"Andrea Bandini, Laura Paladino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-11T13:34:22Z","title":"Fields generated by torsion points of elliptic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2572","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":"sha256:81cf917f7491f4eeb3f2ea73a339b44d2b1e9d9749abd4bf0595e0a1de31d2d8","target":"record","created_at":"2026-05-18T01:58:27Z","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":"684708d81efa587f5cb107f1e7a8569b99a2300733ac4e34359eaa541f6fad18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-11T13:34:22Z","title_canon_sha256":"d63c49365271034464b3876fe0ddd6ce357a158f0e7b3650f71f5b125403bcdd"},"schema_version":"1.0","source":{"id":"1403.2572","kind":"arxiv","version":2}},"canonical_sha256":"237fbaf9eb2c2d8af28272a8ed9e37988359c7c5f77e13d7a625a9bde69808af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"237fbaf9eb2c2d8af28272a8ed9e37988359c7c5f77e13d7a625a9bde69808af","first_computed_at":"2026-05-18T01:58:27.350996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:27.350996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5QndDCxYIeN0YJ4a1prpsQJ0S8Um/t0fvKgWqQUKEFeVCdEiRfOlIKEW/jR+92AV9gF9KXV+Cc9q1Zpu4hnhAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:27.351500Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2572","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81cf917f7491f4eeb3f2ea73a339b44d2b1e9d9749abd4bf0595e0a1de31d2d8","sha256:e6f37fccab2583ffc1f0184cec75090e74040f014f3436589e70d15601e37371"],"state_sha256":"a7a0d0b196144fd336c5ec892440d77bbae866182af5604205102e1a8926a4fc"}