{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EV6A4DBZSXV3SVC3W74I6QICGL","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":"7aa4a885baf800652a89b42916a79950fe673b7ee81cea45c18b96d7f30e18d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-06T08:16:17Z","title_canon_sha256":"ca103910cc9d4ddf5d9dade7fd5c1c4b2b12aee755032d68003ea9a88e10ccd2"},"schema_version":"1.0","source":{"id":"1803.02056","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02056","created_at":"2026-05-18T00:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02056v1","created_at":"2026-05-18T00:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02056","created_at":"2026-05-18T00:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"EV6A4DBZSXV3","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EV6A4DBZSXV3SVC3","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EV6A4DBZ","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:b69b052a2b68c7d879b749706884993232b8a4da6207ac3b080f6f616eb37c5a","target":"graph","created_at":"2026-05-18T00:21:55Z","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 $D<0$ be a fundamental discriminant and denote by $E(D)$ the exponent of the ideal class group $\\text{Cl}(D)$ of $K={\\mathbb Q}(\\sqrt{D})$. Under the assumption that no Siegel zeros exist we compute all such $D$ with $E(D)$ is a divisor of $8$. We compute all $D$ with $|D|\\leq 3.1\\cdot 10^{20}$ such that $E(D)\\leq 8$.","authors_text":"Andreas-Stephan Elsenhans, Florin Nicolae, J\\\"urgen Kl\\\"uners","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-06T08:16:17Z","title":"Imaginary quadratic number fields with class groups of small exponent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02056","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":"sha256:7de2683d9c40ea97fdb5f68be11db0db9711d257d810c46891ceb2b30e2ea20a","target":"record","created_at":"2026-05-18T00:21:55Z","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":"7aa4a885baf800652a89b42916a79950fe673b7ee81cea45c18b96d7f30e18d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-03-06T08:16:17Z","title_canon_sha256":"ca103910cc9d4ddf5d9dade7fd5c1c4b2b12aee755032d68003ea9a88e10ccd2"},"schema_version":"1.0","source":{"id":"1803.02056","kind":"arxiv","version":1}},"canonical_sha256":"257c0e0c3995ebb9545bb7f88f410232c5a3bddacf30cc6efb2958008f697111","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"257c0e0c3995ebb9545bb7f88f410232c5a3bddacf30cc6efb2958008f697111","first_computed_at":"2026-05-18T00:21:55.919085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:55.919085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tSA0i6xiIh+QplOvXPkr23f+LpE7XFJjKfhMIBNHZ/YHgGklyyrpLS1EtVrtzPpk7B+47PwSmmdmwBZ5Sf3zBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:55.919747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02056","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7de2683d9c40ea97fdb5f68be11db0db9711d257d810c46891ceb2b30e2ea20a","sha256:b69b052a2b68c7d879b749706884993232b8a4da6207ac3b080f6f616eb37c5a"],"state_sha256":"60a97928f52a61c76fd31c37461dfa4372d3185787e00a7f34d9977c03e9fdd0"}