{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:THD3PM5ULOOP7WLQKDTLFDGPMD","short_pith_number":"pith:THD3PM5U","schema_version":"1.0","canonical_sha256":"99c7b7b3b45b9cffd97050e6b28ccf60c87599605e4daf2512fa8e3f500cccbc","source":{"kind":"arxiv","id":"1111.4679","version":2},"attestation_state":"computed","paper":{"title":"Heuristics for $p$-class towers of imaginary quadratic fields, with an Appendix by Jonathan Blackhurst","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Farshid Hajir, Michael R. Bush, Nigel Boston","submitted_at":"2011-11-20T21:08:41Z","abstract_excerpt":"Cohen and Lenstra have given a heuristic which, for a fixed odd prime $p$, leads to many interesting predictions about the distribution of $p$-class groups of imaginary quadratic fields. We extend the Cohen-Lenstra heuristic to a non-abelian setting by considering, for each imaginary quadratic field $K$, the Galois group of the $p$-class tower of $K$, i.e. $G_K:=\\mathrm{Gal}(K_\\infty/K)$ where $K_\\infty$ is the maximal unramified $p$-extension of $K$. By class field theory, the maximal abelian quotient of $G_K$ is isomorphic to the $p$-class group of $K$. For integers $c\\geq 1$, we give a heur"},"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":"1111.4679","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-20T21:08:41Z","cross_cats_sorted":[],"title_canon_sha256":"fb3ba20f9888d2bd9cc6ff502184e8b0f128dee8d4cfbc40dbe54e68696ce2e4","abstract_canon_sha256":"86144c370fe557dc24f9cd12e8061e1db79eab00cf53393959376ff1be0307bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:38.568479Z","signature_b64":"OqR5tYj3J1N9nOILKNvfHrdU4LPADrNZcCVNwDWm1JLT0DyslaUDzdlV0qbdeQjxEfB9K9V2SKEAnpr8tAQICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99c7b7b3b45b9cffd97050e6b28ccf60c87599605e4daf2512fa8e3f500cccbc","last_reissued_at":"2026-05-18T02:31:38.567769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:38.567769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Heuristics for $p$-class towers of imaginary quadratic fields, with an Appendix by Jonathan Blackhurst","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Farshid Hajir, Michael R. Bush, Nigel Boston","submitted_at":"2011-11-20T21:08:41Z","abstract_excerpt":"Cohen and Lenstra have given a heuristic which, for a fixed odd prime $p$, leads to many interesting predictions about the distribution of $p$-class groups of imaginary quadratic fields. We extend the Cohen-Lenstra heuristic to a non-abelian setting by considering, for each imaginary quadratic field $K$, the Galois group of the $p$-class tower of $K$, i.e. $G_K:=\\mathrm{Gal}(K_\\infty/K)$ where $K_\\infty$ is the maximal unramified $p$-extension of $K$. By class field theory, the maximal abelian quotient of $G_K$ is isomorphic to the $p$-class group of $K$. For integers $c\\geq 1$, we give a heur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4679","kind":"arxiv","version":2},"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":"1111.4679","created_at":"2026-05-18T02:31:38.567882+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.4679v2","created_at":"2026-05-18T02:31:38.567882+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4679","created_at":"2026-05-18T02:31:38.567882+00:00"},{"alias_kind":"pith_short_12","alias_value":"THD3PM5ULOOP","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"THD3PM5ULOOP7WLQ","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"THD3PM5U","created_at":"2026-05-18T12:26:42.757692+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/THD3PM5ULOOP7WLQKDTLFDGPMD","json":"https://pith.science/pith/THD3PM5ULOOP7WLQKDTLFDGPMD.json","graph_json":"https://pith.science/api/pith-number/THD3PM5ULOOP7WLQKDTLFDGPMD/graph.json","events_json":"https://pith.science/api/pith-number/THD3PM5ULOOP7WLQKDTLFDGPMD/events.json","paper":"https://pith.science/paper/THD3PM5U"},"agent_actions":{"view_html":"https://pith.science/pith/THD3PM5ULOOP7WLQKDTLFDGPMD","download_json":"https://pith.science/pith/THD3PM5ULOOP7WLQKDTLFDGPMD.json","view_paper":"https://pith.science/paper/THD3PM5U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.4679&json=true","fetch_graph":"https://pith.science/api/pith-number/THD3PM5ULOOP7WLQKDTLFDGPMD/graph.json","fetch_events":"https://pith.science/api/pith-number/THD3PM5ULOOP7WLQKDTLFDGPMD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/THD3PM5ULOOP7WLQKDTLFDGPMD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/THD3PM5ULOOP7WLQKDTLFDGPMD/action/storage_attestation","attest_author":"https://pith.science/pith/THD3PM5ULOOP7WLQKDTLFDGPMD/action/author_attestation","sign_citation":"https://pith.science/pith/THD3PM5ULOOP7WLQKDTLFDGPMD/action/citation_signature","submit_replication":"https://pith.science/pith/THD3PM5ULOOP7WLQKDTLFDGPMD/action/replication_record"}},"created_at":"2026-05-18T02:31:38.567882+00:00","updated_at":"2026-05-18T02:31:38.567882+00:00"}