{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:5JY46CLWTF3EVNWO5BIP63RWG3","short_pith_number":"pith:5JY46CLW","schema_version":"1.0","canonical_sha256":"ea71cf097699764ab6cee850ff6e3636da3edee3ea9ff6ce8a1a2c9b6430370d","source":{"kind":"arxiv","id":"1301.1239","version":2},"attestation_state":"computed","paper":{"title":"Cokernels of random matrices satisfy the Cohen-Lenstra heuristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kenneth Maples","submitted_at":"2013-01-07T15:57:52Z","abstract_excerpt":"Let A be an n by n random matrix with iid entries taken from the p-adic integers or Z/NZ. Then under mild non-degeneracy conditions the cokernel of A has a universal probability distribution. In particular, the p-part of an iid random matrix over the integers has cokernel distributed according to the Cohen-Lenstra measure up to an exponentially small error."},"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":"1301.1239","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-07T15:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"e3ada69c624d98f2b0c676cd0df44641ab2e21820148eae629c6b3397c26eacc","abstract_canon_sha256":"43366d66508e983f21e5b4e4cc6f8c49a5f4481272d92e82b03f803e537ccd01"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:13.214428Z","signature_b64":"P5wpgpP7GxXZEAcchAH1Q8QSGgjF4hW+vih6WHrC0kPO/1kII/CGMXbnmmLBfsWeTkfIjSQytBOc774tGXR/Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea71cf097699764ab6cee850ff6e3636da3edee3ea9ff6ce8a1a2c9b6430370d","last_reissued_at":"2026-05-18T03:19:13.213814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:13.213814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cokernels of random matrices satisfy the Cohen-Lenstra heuristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kenneth Maples","submitted_at":"2013-01-07T15:57:52Z","abstract_excerpt":"Let A be an n by n random matrix with iid entries taken from the p-adic integers or Z/NZ. Then under mild non-degeneracy conditions the cokernel of A has a universal probability distribution. In particular, the p-part of an iid random matrix over the integers has cokernel distributed according to the Cohen-Lenstra measure up to an exponentially small error."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1239","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":"1301.1239","created_at":"2026-05-18T03:19:13.213893+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.1239v2","created_at":"2026-05-18T03:19:13.213893+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1239","created_at":"2026-05-18T03:19:13.213893+00:00"},{"alias_kind":"pith_short_12","alias_value":"5JY46CLWTF3E","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"5JY46CLWTF3EVNWO","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"5JY46CLW","created_at":"2026-05-18T12:27:34.582898+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/5JY46CLWTF3EVNWO5BIP63RWG3","json":"https://pith.science/pith/5JY46CLWTF3EVNWO5BIP63RWG3.json","graph_json":"https://pith.science/api/pith-number/5JY46CLWTF3EVNWO5BIP63RWG3/graph.json","events_json":"https://pith.science/api/pith-number/5JY46CLWTF3EVNWO5BIP63RWG3/events.json","paper":"https://pith.science/paper/5JY46CLW"},"agent_actions":{"view_html":"https://pith.science/pith/5JY46CLWTF3EVNWO5BIP63RWG3","download_json":"https://pith.science/pith/5JY46CLWTF3EVNWO5BIP63RWG3.json","view_paper":"https://pith.science/paper/5JY46CLW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.1239&json=true","fetch_graph":"https://pith.science/api/pith-number/5JY46CLWTF3EVNWO5BIP63RWG3/graph.json","fetch_events":"https://pith.science/api/pith-number/5JY46CLWTF3EVNWO5BIP63RWG3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5JY46CLWTF3EVNWO5BIP63RWG3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5JY46CLWTF3EVNWO5BIP63RWG3/action/storage_attestation","attest_author":"https://pith.science/pith/5JY46CLWTF3EVNWO5BIP63RWG3/action/author_attestation","sign_citation":"https://pith.science/pith/5JY46CLWTF3EVNWO5BIP63RWG3/action/citation_signature","submit_replication":"https://pith.science/pith/5JY46CLWTF3EVNWO5BIP63RWG3/action/replication_record"}},"created_at":"2026-05-18T03:19:13.213893+00:00","updated_at":"2026-05-18T03:19:13.213893+00:00"}