{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:V27PU72T45D3VEUS26NKLSHXQV","short_pith_number":"pith:V27PU72T","schema_version":"1.0","canonical_sha256":"aebefa7f53e747ba9292d79aa5c8f7856c9e6fd3590932a00335019a428780fc","source":{"kind":"arxiv","id":"1710.00793","version":3},"attestation_state":"computed","paper":{"title":"Moments of unramified 2-group extensions of quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jack Klys","submitted_at":"2017-10-02T17:03:45Z","abstract_excerpt":"Let $f\\left(K\\right)$ be the number of unramified extensions $L/K$ of a quadratic number field $K$ with $\\mathrm{Gal}\\left(L/K\\right)=H$ and $\\mathrm{Gal}\\left(L/\\mathbb{Q}\\right)=G$ where $G$ is a central extension of $\\mathbb{F}_{2}^{n}$ by $\\mathbb{F}_{2}$. We find a function $g\\left(K\\right)$ such that $f/g$ has finite moments and a distribution on its values. We show this distribution is a point mass when $H$ is non-abelian and the Cohen-Lenstra distribution when $H$ is abelian, despite the fact that the set of values of $f/g$ do not form a discrete set. We prove an explicit formula for $"},"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":"1710.00793","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-02T17:03:45Z","cross_cats_sorted":[],"title_canon_sha256":"12062abf834d83b59b40b9d3607dc02daff1ff6c12ed93aa04a2c9f6dc0e81c1","abstract_canon_sha256":"00a92b6581c4b6749f9e779b9a14132cbf8185f5d2c3537e020a2595d46398df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:32.528993Z","signature_b64":"V4aTub1qdxuAX0wD2SKQyqJYjQNSZnk04UPuBCZvmpaFgi19C3IvD4y05Tf2zxQG8tdO23DzhDJKs8aQjiozCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aebefa7f53e747ba9292d79aa5c8f7856c9e6fd3590932a00335019a428780fc","last_reissued_at":"2026-05-17T23:39:32.528284Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:32.528284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moments of unramified 2-group extensions of quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jack Klys","submitted_at":"2017-10-02T17:03:45Z","abstract_excerpt":"Let $f\\left(K\\right)$ be the number of unramified extensions $L/K$ of a quadratic number field $K$ with $\\mathrm{Gal}\\left(L/K\\right)=H$ and $\\mathrm{Gal}\\left(L/\\mathbb{Q}\\right)=G$ where $G$ is a central extension of $\\mathbb{F}_{2}^{n}$ by $\\mathbb{F}_{2}$. We find a function $g\\left(K\\right)$ such that $f/g$ has finite moments and a distribution on its values. We show this distribution is a point mass when $H$ is non-abelian and the Cohen-Lenstra distribution when $H$ is abelian, despite the fact that the set of values of $f/g$ do not form a discrete set. We prove an explicit formula for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00793","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":"1710.00793","created_at":"2026-05-17T23:39:32.528399+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.00793v3","created_at":"2026-05-17T23:39:32.528399+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00793","created_at":"2026-05-17T23:39:32.528399+00:00"},{"alias_kind":"pith_short_12","alias_value":"V27PU72T45D3","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"V27PU72T45D3VEUS","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"V27PU72T","created_at":"2026-05-18T12:31:49.984773+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.21792","citing_title":"Serre's problem for multiple conics","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V27PU72T45D3VEUS26NKLSHXQV","json":"https://pith.science/pith/V27PU72T45D3VEUS26NKLSHXQV.json","graph_json":"https://pith.science/api/pith-number/V27PU72T45D3VEUS26NKLSHXQV/graph.json","events_json":"https://pith.science/api/pith-number/V27PU72T45D3VEUS26NKLSHXQV/events.json","paper":"https://pith.science/paper/V27PU72T"},"agent_actions":{"view_html":"https://pith.science/pith/V27PU72T45D3VEUS26NKLSHXQV","download_json":"https://pith.science/pith/V27PU72T45D3VEUS26NKLSHXQV.json","view_paper":"https://pith.science/paper/V27PU72T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.00793&json=true","fetch_graph":"https://pith.science/api/pith-number/V27PU72T45D3VEUS26NKLSHXQV/graph.json","fetch_events":"https://pith.science/api/pith-number/V27PU72T45D3VEUS26NKLSHXQV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V27PU72T45D3VEUS26NKLSHXQV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V27PU72T45D3VEUS26NKLSHXQV/action/storage_attestation","attest_author":"https://pith.science/pith/V27PU72T45D3VEUS26NKLSHXQV/action/author_attestation","sign_citation":"https://pith.science/pith/V27PU72T45D3VEUS26NKLSHXQV/action/citation_signature","submit_replication":"https://pith.science/pith/V27PU72T45D3VEUS26NKLSHXQV/action/replication_record"}},"created_at":"2026-05-17T23:39:32.528399+00:00","updated_at":"2026-05-17T23:39:32.528399+00:00"}