{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:OCV5E6FJU7FSJ5QUBAREQFYCDK","short_pith_number":"pith:OCV5E6FJ","schema_version":"1.0","canonical_sha256":"70abd278a9a7cb24f61408224817021ab5803fd0b41458e9e87800b06889509f","source":{"kind":"arxiv","id":"1907.05002","version":2},"attestation_state":"computed","paper":{"title":"A predicted distribution for Galois groups of maximal unramified extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Zureick-Brown, Melanie Matchett Wood, Yuan Liu","submitted_at":"2019-07-11T05:31:33Z","abstract_excerpt":"We consider the distribution of the Galois groups $\\operatorname{Gal}(K^{\\operatorname{un}}/K)$ of maximal unramified extensions as $K$ ranges over $\\Gamma$-extensions of $\\mathbb{Q}$ or $\\mathbb{F}_q(t)$. We prove two properties of $\\operatorname{Gal}(K^{\\operatorname{un}}/K)$ coming from number theory, which we use as motivation to build a probability distribution on profinite groups with these properties. In Part I, we build such a distribution as a limit of distributions on $n$-generated profinite groups. In Part II, we prove as $q\\rightarrow\\infty$, agreement of $\\operatorname{Gal}(K^{\\op"},"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":"1907.05002","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-11T05:31:33Z","cross_cats_sorted":[],"title_canon_sha256":"2e3396e1a12e88584d65988ff559174935b71cf78f56e6acaa9317e1ab820d80","abstract_canon_sha256":"0c4d77e336fe6aaec20a06b972a7610c695021610e56c8682a63cc0dec8dba1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:42:11.943372Z","signature_b64":"axX7A1L8wg2zZFyNs4QLD/8O4t2x2cRk33AGWuwlczVsFGkmJscyDJ1nZMdj2jTGV6Gjw90oNQojysLHRgq+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70abd278a9a7cb24f61408224817021ab5803fd0b41458e9e87800b06889509f","last_reissued_at":"2026-07-05T04:42:11.942859Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:42:11.942859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A predicted distribution for Galois groups of maximal unramified extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Zureick-Brown, Melanie Matchett Wood, Yuan Liu","submitted_at":"2019-07-11T05:31:33Z","abstract_excerpt":"We consider the distribution of the Galois groups $\\operatorname{Gal}(K^{\\operatorname{un}}/K)$ of maximal unramified extensions as $K$ ranges over $\\Gamma$-extensions of $\\mathbb{Q}$ or $\\mathbb{F}_q(t)$. We prove two properties of $\\operatorname{Gal}(K^{\\operatorname{un}}/K)$ coming from number theory, which we use as motivation to build a probability distribution on profinite groups with these properties. In Part I, we build such a distribution as a limit of distributions on $n$-generated profinite groups. In Part II, we prove as $q\\rightarrow\\infty$, agreement of $\\operatorname{Gal}(K^{\\op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05002","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.05002/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1907.05002","created_at":"2026-07-05T04:42:11.942923+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.05002v2","created_at":"2026-07-05T04:42:11.942923+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05002","created_at":"2026-07-05T04:42:11.942923+00:00"},{"alias_kind":"pith_short_12","alias_value":"OCV5E6FJU7FS","created_at":"2026-07-05T04:42:11.942923+00:00"},{"alias_kind":"pith_short_16","alias_value":"OCV5E6FJU7FSJ5QU","created_at":"2026-07-05T04:42:11.942923+00:00"},{"alias_kind":"pith_short_8","alias_value":"OCV5E6FJ","created_at":"2026-07-05T04:42:11.942923+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.04261","citing_title":"Counterexamples for T\\\"urkelli's Modification on Malle's Conjecture","ref_index":2024,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OCV5E6FJU7FSJ5QUBAREQFYCDK","json":"https://pith.science/pith/OCV5E6FJU7FSJ5QUBAREQFYCDK.json","graph_json":"https://pith.science/api/pith-number/OCV5E6FJU7FSJ5QUBAREQFYCDK/graph.json","events_json":"https://pith.science/api/pith-number/OCV5E6FJU7FSJ5QUBAREQFYCDK/events.json","paper":"https://pith.science/paper/OCV5E6FJ"},"agent_actions":{"view_html":"https://pith.science/pith/OCV5E6FJU7FSJ5QUBAREQFYCDK","download_json":"https://pith.science/pith/OCV5E6FJU7FSJ5QUBAREQFYCDK.json","view_paper":"https://pith.science/paper/OCV5E6FJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.05002&json=true","fetch_graph":"https://pith.science/api/pith-number/OCV5E6FJU7FSJ5QUBAREQFYCDK/graph.json","fetch_events":"https://pith.science/api/pith-number/OCV5E6FJU7FSJ5QUBAREQFYCDK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OCV5E6FJU7FSJ5QUBAREQFYCDK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OCV5E6FJU7FSJ5QUBAREQFYCDK/action/storage_attestation","attest_author":"https://pith.science/pith/OCV5E6FJU7FSJ5QUBAREQFYCDK/action/author_attestation","sign_citation":"https://pith.science/pith/OCV5E6FJU7FSJ5QUBAREQFYCDK/action/citation_signature","submit_replication":"https://pith.science/pith/OCV5E6FJU7FSJ5QUBAREQFYCDK/action/replication_record"}},"created_at":"2026-07-05T04:42:11.942923+00:00","updated_at":"2026-07-05T04:42:11.942923+00:00"}