{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5F54MOWH4ZJB7KA2X2YWJU3MIT","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":"8533c9ceca12624026565882cdfd7f23bc74c3042784b796934c43cdd8a62495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-10T22:26:34Z","title_canon_sha256":"2bdaeab61659ad99b813ac5134436e4706e4e96446ba6c201abb37678fcdfc3b"},"schema_version":"1.0","source":{"id":"1410.2921","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2921","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2921v4","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2921","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"5F54MOWH4ZJB","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5F54MOWH4ZJB7KA2","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5F54MOWH","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:17f8548b8cadf1bc231df64240068d176a7b251bb7e26892118bad660db2f4a0","target":"graph","created_at":"2026-05-18T02:30:15Z","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":"For any prime p and any positive integer n, let B(p,n) denote the n-th layer of the cyclotomic Z_p-extension over the rationals. Based on the heuristics of Cohen and Lenstra, and refined by new results on class numbers of particular B(p,n), we provide evidence for the following conjecture: For all primes p and positive integers n, the ideal class group of B(p,n) is trivial.","authors_text":"John C. Miller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-10T22:26:34Z","title":"Class numbers in cyclotomic Z_p-extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2921","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":"sha256:8d62b2fcb487a26803deab714470bcc64d02416f7598e3fdadb7f8e655d0fd5b","target":"record","created_at":"2026-05-18T02:30:15Z","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":"8533c9ceca12624026565882cdfd7f23bc74c3042784b796934c43cdd8a62495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-10T22:26:34Z","title_canon_sha256":"2bdaeab61659ad99b813ac5134436e4706e4e96446ba6c201abb37678fcdfc3b"},"schema_version":"1.0","source":{"id":"1410.2921","kind":"arxiv","version":4}},"canonical_sha256":"e97bc63ac7e6521fa81abeb164d36c44d29332548b9af0097b8f3df2b8e1e1c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e97bc63ac7e6521fa81abeb164d36c44d29332548b9af0097b8f3df2b8e1e1c3","first_computed_at":"2026-05-18T02:30:15.253134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:15.253134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V0/hQyuZbBVRIALeHoKR2KqVvbJb88sWiFFvwvzaTgzxLI/ElmzFCtabhuaH8AqZEGS825m1WjSbS1OTgQQzDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:15.253587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2921","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d62b2fcb487a26803deab714470bcc64d02416f7598e3fdadb7f8e655d0fd5b","sha256:17f8548b8cadf1bc231df64240068d176a7b251bb7e26892118bad660db2f4a0"],"state_sha256":"806b0751e4e0dbe4e10dc637e375083bbc4cd3840b5d01b202a747b18b01bf4b"}