{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:XKD3SQXMC2EOEQCNDTXJKWA6QS","short_pith_number":"pith:XKD3SQXM","schema_version":"1.0","canonical_sha256":"ba87b942ec1688e2404d1cee95581e848244adaa84db24d3c30856504ca0b787","source":{"kind":"arxiv","id":"2006.04934","version":3},"attestation_state":"computed","paper":{"title":"Identifying measures on non-abelian groups and modules by their moments via reduction to a local problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.NT","authors_text":"Will Sawin","submitted_at":"2020-06-08T21:04:08Z","abstract_excerpt":"Work on generalizations of the Cohen-Lenstra and Cohen-Martinet heuristics has drawn attention to probability measures on the space of isomorphism classes of profinite groups. As is common in probability theory, it would be desirable to know that these measures are determined by their moments, which in this context are the expected number of surjections to a fixed finite group. We show a wide class of measures, including those appearing in a recent paper of Liu, Wood, and Zurieck-Brown, have this property. The method is to work \"locally\" with groups that are extensions of a fixed group by a pr"},"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":"2006.04934","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-06-08T21:04:08Z","cross_cats_sorted":["math.GR","math.PR"],"title_canon_sha256":"9c508df1e582bb7a902bb7dc4b1ee5b1f9da78bd55b8dabf00e17ab5f72d8312","abstract_canon_sha256":"094a261200c225c2841f6d84f3b6d1d19b4d5b36d91a1c733249c0b1d64a4d2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:28:58.422209Z","signature_b64":"zyPldfRCNfSC09WJ1F/UR1VK+oFksVq0Q3bp82Ft8LhQO+dRhytQvzzHB40QqXpJbySEYSXtVp0hLIkEDmffBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba87b942ec1688e2404d1cee95581e848244adaa84db24d3c30856504ca0b787","last_reissued_at":"2026-07-05T05:28:58.421803Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:28:58.421803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Identifying measures on non-abelian groups and modules by their moments via reduction to a local problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.NT","authors_text":"Will Sawin","submitted_at":"2020-06-08T21:04:08Z","abstract_excerpt":"Work on generalizations of the Cohen-Lenstra and Cohen-Martinet heuristics has drawn attention to probability measures on the space of isomorphism classes of profinite groups. As is common in probability theory, it would be desirable to know that these measures are determined by their moments, which in this context are the expected number of surjections to a fixed finite group. We show a wide class of measures, including those appearing in a recent paper of Liu, Wood, and Zurieck-Brown, have this property. The method is to work \"locally\" with groups that are extensions of a fixed group by a pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.04934","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.04934/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":"2006.04934","created_at":"2026-07-05T05:28:58.421855+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.04934v3","created_at":"2026-07-05T05:28:58.421855+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.04934","created_at":"2026-07-05T05:28:58.421855+00:00"},{"alias_kind":"pith_short_12","alias_value":"XKD3SQXMC2EO","created_at":"2026-07-05T05:28:58.421855+00:00"},{"alias_kind":"pith_short_16","alias_value":"XKD3SQXMC2EOEQCN","created_at":"2026-07-05T05:28:58.421855+00:00"},{"alias_kind":"pith_short_8","alias_value":"XKD3SQXM","created_at":"2026-07-05T05:28:58.421855+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.21558","citing_title":"The imaginary case of the nonabelian Cohen--Lenstra heuristics","ref_index":2016,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XKD3SQXMC2EOEQCNDTXJKWA6QS","json":"https://pith.science/pith/XKD3SQXMC2EOEQCNDTXJKWA6QS.json","graph_json":"https://pith.science/api/pith-number/XKD3SQXMC2EOEQCNDTXJKWA6QS/graph.json","events_json":"https://pith.science/api/pith-number/XKD3SQXMC2EOEQCNDTXJKWA6QS/events.json","paper":"https://pith.science/paper/XKD3SQXM"},"agent_actions":{"view_html":"https://pith.science/pith/XKD3SQXMC2EOEQCNDTXJKWA6QS","download_json":"https://pith.science/pith/XKD3SQXMC2EOEQCNDTXJKWA6QS.json","view_paper":"https://pith.science/paper/XKD3SQXM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.04934&json=true","fetch_graph":"https://pith.science/api/pith-number/XKD3SQXMC2EOEQCNDTXJKWA6QS/graph.json","fetch_events":"https://pith.science/api/pith-number/XKD3SQXMC2EOEQCNDTXJKWA6QS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XKD3SQXMC2EOEQCNDTXJKWA6QS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XKD3SQXMC2EOEQCNDTXJKWA6QS/action/storage_attestation","attest_author":"https://pith.science/pith/XKD3SQXMC2EOEQCNDTXJKWA6QS/action/author_attestation","sign_citation":"https://pith.science/pith/XKD3SQXMC2EOEQCNDTXJKWA6QS/action/citation_signature","submit_replication":"https://pith.science/pith/XKD3SQXMC2EOEQCNDTXJKWA6QS/action/replication_record"}},"created_at":"2026-07-05T05:28:58.421855+00:00","updated_at":"2026-07-05T05:28:58.421855+00:00"}