{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZOLJL5U37UMOQ44MHH3FEOH7JM","short_pith_number":"pith:ZOLJL5U3","schema_version":"1.0","canonical_sha256":"cb9695f69bfd18e8738c39f65238ff4b27ad5e35f335cd49ffba0ec862c49600","source":{"kind":"arxiv","id":"1405.1795","version":1},"attestation_state":"computed","paper":{"title":"Nilpotent-independent sets and estimation in matrix algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Brian P. Corr, Cheryl E. Praeger, Tomasz Popiel","submitted_at":"2014-05-08T03:13:58Z","abstract_excerpt":"Efficient methods for computing with matrices over finite fields often involve randomised algorithms, where matrices with a certain property are sought via repeated random selection. Complexity analyses for these algorithms require knowledge of the proportion of relevant matrices in the ambient group or algebra. We introduce a method for estimating proportions of families $N$ of elements in the algebra of all $d\\times d$ matrices over a field of order $q$, where membership of a matrix in $N$ depends only on its `invertible part'. The method is based on estimating proportions of certain subsets"},"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":"1405.1795","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-08T03:13:58Z","cross_cats_sorted":[],"title_canon_sha256":"9eb70cc76cea0b8a5d90b700dcc2773b848eabd20b3e8ef68a75faf04df6c74d","abstract_canon_sha256":"ce9f9a0e217bbe8bd8ea9bdfcdff883e75b6d572473aa0874ebe2efc58a79e0d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:14.438256Z","signature_b64":"HjkBvFO45bKNky7HAcSAUzfpwLpd4ywip9uvjJrgLLv1wsyLGj97YMcFlOLWvdpAk8CzHhk/6gj8inHvCpIvAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb9695f69bfd18e8738c39f65238ff4b27ad5e35f335cd49ffba0ec862c49600","last_reissued_at":"2026-05-17T23:53:14.437622Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:14.437622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nilpotent-independent sets and estimation in matrix algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Brian P. Corr, Cheryl E. Praeger, Tomasz Popiel","submitted_at":"2014-05-08T03:13:58Z","abstract_excerpt":"Efficient methods for computing with matrices over finite fields often involve randomised algorithms, where matrices with a certain property are sought via repeated random selection. Complexity analyses for these algorithms require knowledge of the proportion of relevant matrices in the ambient group or algebra. We introduce a method for estimating proportions of families $N$ of elements in the algebra of all $d\\times d$ matrices over a field of order $q$, where membership of a matrix in $N$ depends only on its `invertible part'. The method is based on estimating proportions of certain subsets"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1795","kind":"arxiv","version":1},"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":"1405.1795","created_at":"2026-05-17T23:53:14.437714+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.1795v1","created_at":"2026-05-17T23:53:14.437714+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1795","created_at":"2026-05-17T23:53:14.437714+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZOLJL5U37UMO","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZOLJL5U37UMOQ44M","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZOLJL5U3","created_at":"2026-05-18T12:28:59.999130+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/ZOLJL5U37UMOQ44MHH3FEOH7JM","json":"https://pith.science/pith/ZOLJL5U37UMOQ44MHH3FEOH7JM.json","graph_json":"https://pith.science/api/pith-number/ZOLJL5U37UMOQ44MHH3FEOH7JM/graph.json","events_json":"https://pith.science/api/pith-number/ZOLJL5U37UMOQ44MHH3FEOH7JM/events.json","paper":"https://pith.science/paper/ZOLJL5U3"},"agent_actions":{"view_html":"https://pith.science/pith/ZOLJL5U37UMOQ44MHH3FEOH7JM","download_json":"https://pith.science/pith/ZOLJL5U37UMOQ44MHH3FEOH7JM.json","view_paper":"https://pith.science/paper/ZOLJL5U3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.1795&json=true","fetch_graph":"https://pith.science/api/pith-number/ZOLJL5U37UMOQ44MHH3FEOH7JM/graph.json","fetch_events":"https://pith.science/api/pith-number/ZOLJL5U37UMOQ44MHH3FEOH7JM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZOLJL5U37UMOQ44MHH3FEOH7JM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZOLJL5U37UMOQ44MHH3FEOH7JM/action/storage_attestation","attest_author":"https://pith.science/pith/ZOLJL5U37UMOQ44MHH3FEOH7JM/action/author_attestation","sign_citation":"https://pith.science/pith/ZOLJL5U37UMOQ44MHH3FEOH7JM/action/citation_signature","submit_replication":"https://pith.science/pith/ZOLJL5U37UMOQ44MHH3FEOH7JM/action/replication_record"}},"created_at":"2026-05-17T23:53:14.437714+00:00","updated_at":"2026-05-17T23:53:14.437714+00:00"}