{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YVSZVCMNXB5CR2CNTDMNIXZ7WB","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":"455bae8f8698c91e1eb8bf76244f7e97ccfdf978a3bc6b34143c789aacb57277","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-03T21:36:32Z","title_canon_sha256":"0c849a3d1233c5c55e66bf6e10a4111123191d7d81dc5ef0eee6982a1b8d895a"},"schema_version":"1.0","source":{"id":"1511.01126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01126","created_at":"2026-05-18T01:27:48Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01126v1","created_at":"2026-05-18T01:27:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01126","created_at":"2026-05-18T01:27:48Z"},{"alias_kind":"pith_short_12","alias_value":"YVSZVCMNXB5C","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YVSZVCMNXB5CR2CN","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YVSZVCMN","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:95c926a432cf78ddb6f07f08d29d70c448117178fd2330e28085e05b1c4d947c","target":"graph","created_at":"2026-05-18T01:27:48Z","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 $E$ be an elliptic curve defined over $\\mathbb{Q}$, and let $K$ be a number field of degree four that is Galois over $\\mathbb{Q}$. The goal of this article is to classify the different isomorphism types of $E(K)_{\\text{tors}}$.","authors_text":"Michael Chou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-03T21:36:32Z","title":"Torsion of rational elliptic curves over quartic Galois number fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01126","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":"sha256:985225427d3a6353d0ec4778093887ec23fd05ceb54aaa3b43a4cc02e87591d4","target":"record","created_at":"2026-05-18T01:27:48Z","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":"455bae8f8698c91e1eb8bf76244f7e97ccfdf978a3bc6b34143c789aacb57277","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-03T21:36:32Z","title_canon_sha256":"0c849a3d1233c5c55e66bf6e10a4111123191d7d81dc5ef0eee6982a1b8d895a"},"schema_version":"1.0","source":{"id":"1511.01126","kind":"arxiv","version":1}},"canonical_sha256":"c5659a898db87a28e84d98d8d45f3fb05456e4ca9f6df27247ee4ab49a1cd9cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5659a898db87a28e84d98d8d45f3fb05456e4ca9f6df27247ee4ab49a1cd9cc","first_computed_at":"2026-05-18T01:27:48.021939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:48.021939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1DQbrcaXpY8zSbho9ZHDvP+9XzvMto6kUduXw+DRwSL/XW6P9oEJdEPLSSiIjtGjOrCWFac7e60YnKdkKnLHCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:48.022654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:985225427d3a6353d0ec4778093887ec23fd05ceb54aaa3b43a4cc02e87591d4","sha256:95c926a432cf78ddb6f07f08d29d70c448117178fd2330e28085e05b1c4d947c"],"state_sha256":"e23c3fcc6b97f32fcd350d01e5aa89c0452efdb9d19b0636b506f8735b24c653"}