{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CGFZBZBQCOOVPTIZT4KTWRSRQT","short_pith_number":"pith:CGFZBZBQ","schema_version":"1.0","canonical_sha256":"118b90e430139d57cd199f153b465184cc630f76a7a88978613f0383b5bb0cdf","source":{"kind":"arxiv","id":"1406.5826","version":1},"attestation_state":"computed","paper":{"title":"The asymptotic complexity of matrix reduction over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cs.DS","authors_text":"Demetres Christofides","submitted_at":"2014-06-23T08:03:23Z","abstract_excerpt":"Consider an invertible n \\times n matrix over some field. The Gauss-Jordan elimination reduces this matrix to the identity matrix using at most n^2 row operations and in general that many operations might be needed.\n  In [1] the authors considered matrices in GL(n;q), the set of n \\times n invertible matrices in the finite field of q elements, and provided an algorithm using only row operations which performs asymptotically better than the Gauss-Jordan elimination. More specifically their `striped elimination algorithm' has asymptotic complexity \\frac{n^2}{\\log_q{n}}. Furthermore they proved t"},"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":"1406.5826","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-06-23T08:03:23Z","cross_cats_sorted":["cs.CC","math.CO"],"title_canon_sha256":"ad943778843e1ecd965003b36308f9123d36426507f25f8ec7692bedf71066e2","abstract_canon_sha256":"efc74bbea9c0ecfdd3d1c7d9096e33db82f207e48d2d129323e0cb3b25fbbebf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:04.140208Z","signature_b64":"0gDlxz6mu4wPnKiHn/KTsCOM2ZiyE6QZLWRQf0Xn8Ptx9o47Wj2mp/zK1iQJT77OXTMvTy1jndi+4TOSexaUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"118b90e430139d57cd199f153b465184cc630f76a7a88978613f0383b5bb0cdf","last_reissued_at":"2026-05-18T02:49:04.139828Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:04.139828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The asymptotic complexity of matrix reduction over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cs.DS","authors_text":"Demetres Christofides","submitted_at":"2014-06-23T08:03:23Z","abstract_excerpt":"Consider an invertible n \\times n matrix over some field. The Gauss-Jordan elimination reduces this matrix to the identity matrix using at most n^2 row operations and in general that many operations might be needed.\n  In [1] the authors considered matrices in GL(n;q), the set of n \\times n invertible matrices in the finite field of q elements, and provided an algorithm using only row operations which performs asymptotically better than the Gauss-Jordan elimination. More specifically their `striped elimination algorithm' has asymptotic complexity \\frac{n^2}{\\log_q{n}}. Furthermore they proved t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5826","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":"1406.5826","created_at":"2026-05-18T02:49:04.139883+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.5826v1","created_at":"2026-05-18T02:49:04.139883+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5826","created_at":"2026-05-18T02:49:04.139883+00:00"},{"alias_kind":"pith_short_12","alias_value":"CGFZBZBQCOOV","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CGFZBZBQCOOVPTIZ","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CGFZBZBQ","created_at":"2026-05-18T12:28:22.404517+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/CGFZBZBQCOOVPTIZT4KTWRSRQT","json":"https://pith.science/pith/CGFZBZBQCOOVPTIZT4KTWRSRQT.json","graph_json":"https://pith.science/api/pith-number/CGFZBZBQCOOVPTIZT4KTWRSRQT/graph.json","events_json":"https://pith.science/api/pith-number/CGFZBZBQCOOVPTIZT4KTWRSRQT/events.json","paper":"https://pith.science/paper/CGFZBZBQ"},"agent_actions":{"view_html":"https://pith.science/pith/CGFZBZBQCOOVPTIZT4KTWRSRQT","download_json":"https://pith.science/pith/CGFZBZBQCOOVPTIZT4KTWRSRQT.json","view_paper":"https://pith.science/paper/CGFZBZBQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.5826&json=true","fetch_graph":"https://pith.science/api/pith-number/CGFZBZBQCOOVPTIZT4KTWRSRQT/graph.json","fetch_events":"https://pith.science/api/pith-number/CGFZBZBQCOOVPTIZT4KTWRSRQT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CGFZBZBQCOOVPTIZT4KTWRSRQT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CGFZBZBQCOOVPTIZT4KTWRSRQT/action/storage_attestation","attest_author":"https://pith.science/pith/CGFZBZBQCOOVPTIZT4KTWRSRQT/action/author_attestation","sign_citation":"https://pith.science/pith/CGFZBZBQCOOVPTIZT4KTWRSRQT/action/citation_signature","submit_replication":"https://pith.science/pith/CGFZBZBQCOOVPTIZT4KTWRSRQT/action/replication_record"}},"created_at":"2026-05-18T02:49:04.139883+00:00","updated_at":"2026-05-18T02:49:04.139883+00:00"}