{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:43VK7PGIY5GPQPEGTYERMOE5C5","short_pith_number":"pith:43VK7PGI","schema_version":"1.0","canonical_sha256":"e6eaafbcc8c74cf83c869e0916389d176c00cf30ce5802beffb022247c00e7e0","source":{"kind":"arxiv","id":"1402.5997","version":3},"attestation_state":"computed","paper":{"title":"Elliptic curves over $\\mathbb{Q}$ and 2-adic images of Galois","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Zureick-Brown, Jeremy Rouse","submitted_at":"2014-02-24T21:54:41Z","abstract_excerpt":"We give a classification of all possible $2$-adic images of Galois representations associated to elliptic curves over $\\mathbb{Q}$. To this end, we compute the 'arithmetically maximal' tower of 2-power level modular curves, develop techniques to compute their equations, and classify the rational points on these curves."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.5997","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-24T21:54:41Z","cross_cats_sorted":[],"title_canon_sha256":"1378a069d7ab0179d75b7a53eb126e3803f8bcfacab7e78d8a9e8926ba493289","abstract_canon_sha256":"58d10a23c4ac8ad626730775503df548c451aed32ddd2eb47da483003fbd86b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:35.246112Z","signature_b64":"KvaoLlB9E2Koc6T39BEqYNaUj6KeN0xw0yceeeN777x3yiPzNeExHpAYSIpQQHpcSjhwu03B0iqll8h9nfjYAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6eaafbcc8c74cf83c869e0916389d176c00cf30ce5802beffb022247c00e7e0","last_reissued_at":"2026-05-18T00:25:35.245170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:35.245170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elliptic curves over $\\mathbb{Q}$ and 2-adic images of Galois","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Zureick-Brown, Jeremy Rouse","submitted_at":"2014-02-24T21:54:41Z","abstract_excerpt":"We give a classification of all possible $2$-adic images of Galois representations associated to elliptic curves over $\\mathbb{Q}$. To this end, we compute the 'arithmetically maximal' tower of 2-power level modular curves, develop techniques to compute their equations, and classify the rational points on these curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5997","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.5997","created_at":"2026-05-18T00:25:35.245330+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.5997v3","created_at":"2026-05-18T00:25:35.245330+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5997","created_at":"2026-05-18T00:25:35.245330+00:00"},{"alias_kind":"pith_short_12","alias_value":"43VK7PGIY5GP","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"43VK7PGIY5GPQPEG","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"43VK7PGI","created_at":"2026-05-18T12:28:11.866339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/43VK7PGIY5GPQPEGTYERMOE5C5","json":"https://pith.science/pith/43VK7PGIY5GPQPEGTYERMOE5C5.json","graph_json":"https://pith.science/api/pith-number/43VK7PGIY5GPQPEGTYERMOE5C5/graph.json","events_json":"https://pith.science/api/pith-number/43VK7PGIY5GPQPEGTYERMOE5C5/events.json","paper":"https://pith.science/paper/43VK7PGI"},"agent_actions":{"view_html":"https://pith.science/pith/43VK7PGIY5GPQPEGTYERMOE5C5","download_json":"https://pith.science/pith/43VK7PGIY5GPQPEGTYERMOE5C5.json","view_paper":"https://pith.science/paper/43VK7PGI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.5997&json=true","fetch_graph":"https://pith.science/api/pith-number/43VK7PGIY5GPQPEGTYERMOE5C5/graph.json","fetch_events":"https://pith.science/api/pith-number/43VK7PGIY5GPQPEGTYERMOE5C5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/43VK7PGIY5GPQPEGTYERMOE5C5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/43VK7PGIY5GPQPEGTYERMOE5C5/action/storage_attestation","attest_author":"https://pith.science/pith/43VK7PGIY5GPQPEGTYERMOE5C5/action/author_attestation","sign_citation":"https://pith.science/pith/43VK7PGIY5GPQPEGTYERMOE5C5/action/citation_signature","submit_replication":"https://pith.science/pith/43VK7PGIY5GPQPEGTYERMOE5C5/action/replication_record"}},"created_at":"2026-05-18T00:25:35.245330+00:00","updated_at":"2026-05-18T00:25:35.245330+00:00"}