{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3HASYBWDRO3OR2TTQJONXWT2LW","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":"22646d341f8f6ebad1967ed4461b963968fef340c998af8e075a005fd15b33b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-17T07:43:23Z","title_canon_sha256":"22fbf4d11aa17dc723237eb276493bdde1a42a4953c671fa8f67ca9e342bee01"},"schema_version":"1.0","source":{"id":"1611.05595","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.05595","created_at":"2026-05-18T00:43:01Z"},{"alias_kind":"arxiv_version","alias_value":"1611.05595v2","created_at":"2026-05-18T00:43:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.05595","created_at":"2026-05-18T00:43:01Z"},{"alias_kind":"pith_short_12","alias_value":"3HASYBWDRO3O","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3HASYBWDRO3OR2TT","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3HASYBWD","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:57a7dd17168ba88cb32cc827550386a3568b90c7ddaccd0e4964ef0ff7b82891","target":"graph","created_at":"2026-05-18T00:43:01Z","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":"We compute all the moments of a normalization of the function which counts unramified $H_{8}$-extensions of quadratic fields, where $H_{8}$ is the quaternion group of order 8, and show that the values of this function determine a constant distribution. Furthermore we propose a similar modification to the non-abelian Cohen-Lenstra heuristics for unramified G-extensions of quadratic fields for G in a large class of 2-groups, which we conjecture will give finite moments which determine a distribution. Our method additionally can be used to determine the asymptotics of the unnormalized counting fu","authors_text":"Brandon Alberts, Jack Klys","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-17T07:43:23Z","title":"The distribution of $H_{8}$-extensions of quadratic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05595","kind":"arxiv","version":2},"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:cb075bef0125943e3bf198ada3bc18148cdcef7f795535f3d9477ee16121c486","target":"record","created_at":"2026-05-18T00:43:01Z","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":"22646d341f8f6ebad1967ed4461b963968fef340c998af8e075a005fd15b33b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-17T07:43:23Z","title_canon_sha256":"22fbf4d11aa17dc723237eb276493bdde1a42a4953c671fa8f67ca9e342bee01"},"schema_version":"1.0","source":{"id":"1611.05595","kind":"arxiv","version":2}},"canonical_sha256":"d9c12c06c38bb6e8ea73825cdbda7a5db09898197d1438051f02ae55aacf4fab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9c12c06c38bb6e8ea73825cdbda7a5db09898197d1438051f02ae55aacf4fab","first_computed_at":"2026-05-18T00:43:01.794655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:01.794655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sDTe6si++6RwyKJC6oXJJjbEeIe0poYSDVYz4XdzFKLX1VcNwLVdIpENW8F24ZJdFp121meaz/gZFxzpwEorBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:01.795292Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.05595","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb075bef0125943e3bf198ada3bc18148cdcef7f795535f3d9477ee16121c486","sha256:57a7dd17168ba88cb32cc827550386a3568b90c7ddaccd0e4964ef0ff7b82891"],"state_sha256":"4ced8eec728f2db056598e14f59655d5dc0659e8b53c29536d5386bd8b4ef859"}