{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:PAJAREEOPWDE44HYMO3L7CREFL","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":"95843ca0f9f5a1317d187c265ee24a89f7cb0ef4c2aff3f8d475b7973d727ffb","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-09T10:59:46Z","title_canon_sha256":"78914a584be04cbd8d4bd268ce2ecb5d5183376bdceed3e97d92c4fd91bf467f"},"schema_version":"1.0","source":{"id":"0805.1231","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.1231","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"arxiv_version","alias_value":"0805.1231v4","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.1231","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"pith_short_12","alias_value":"PAJAREEOPWDE","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"PAJAREEOPWDE44HY","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"PAJAREEO","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:d66b6ab061753460a7012462b17d1b98cabaae8576ae7cc5e3a3d12598d98f71","target":"graph","created_at":"2026-05-18T01:30:43Z","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 p be a prime number and M a quadratic number field, M not equal to Q(\\sqrt{p}) if p is congruent to 1 modulo 4. We will prove that for any positive integer d there exists a Galois extension F/Q with Galois group D_{2p} and an elliptic curve E/Q such that F contains M and the p-Selmer group of E/F has size at least p^d.","authors_text":"Alex Bartel","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-09T10:59:46Z","title":"Large Selmer groups over number fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1231","kind":"arxiv","version":4},"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":"sha256:269ce706d5ffeaf06d0c8cb2757b34a423280e913be86434e100a0938c46e623","target":"record","created_at":"2026-05-18T01:30:43Z","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":"95843ca0f9f5a1317d187c265ee24a89f7cb0ef4c2aff3f8d475b7973d727ffb","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-05-09T10:59:46Z","title_canon_sha256":"78914a584be04cbd8d4bd268ce2ecb5d5183376bdceed3e97d92c4fd91bf467f"},"schema_version":"1.0","source":{"id":"0805.1231","kind":"arxiv","version":4}},"canonical_sha256":"781208908e7d864e70f863b6bf8a242af5316eb0d683f5bad232667957c7474a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"781208908e7d864e70f863b6bf8a242af5316eb0d683f5bad232667957c7474a","first_computed_at":"2026-05-18T01:30:43.650685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:43.650685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8HXfYqe+3FfvH6vSHQ9Ks5OPcvgzgpzfEcSNCNzjvZs6a1fJnXGytK3Oi0vHIREJiNzNmrjVWyDT1lUd25sYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:43.651330Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.1231","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:269ce706d5ffeaf06d0c8cb2757b34a423280e913be86434e100a0938c46e623","sha256:d66b6ab061753460a7012462b17d1b98cabaae8576ae7cc5e3a3d12598d98f71"],"state_sha256":"28ced23b89bc0a97828f3fdca35e9d5906df1511ab9f0fe348c0675f55727ab0"}