{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:2Q4G2WHMP44C7KLSZTFF22I5MD","short_pith_number":"pith:2Q4G2WHM","schema_version":"1.0","canonical_sha256":"d4386d58ec7f382fa972ccca5d691d60e5a41ab02a9c655cfefb61f45c4d1b7a","source":{"kind":"arxiv","id":"1903.08326","version":2},"attestation_state":"computed","paper":{"title":"Numerically Stable Polynomially Coded Computing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mohammad Fahim, Viveck R. Cadambe","submitted_at":"2019-03-20T03:24:53Z","abstract_excerpt":"We study the numerical stability of polynomial based encoding methods, which has emerged to be a powerful class of techniques for providing straggler and fault tolerance in the area of coded computing. Our contributions are as follows: 1) We construct new codes for matrix multiplication that achieve the same fault/straggler tolerance as the previously constructed MatDot Codes and Polynomial Codes. Unlike previous codes that use polynomials expanded in a monomial basis, our codes uses a basis of orthogonal polynomials. 2) We show that the condition number of every $m \\times m$ sub-matrix of an "},"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":"1903.08326","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-03-20T03:24:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7b41f28316727e2cf0a442a7679bf3aaf748b446be7728b1f417fd37272a334d","abstract_canon_sha256":"45932bcf6752b8fc95c7e971b06b2dae9a4de4654a6b21f895227e665200099e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:22.324600Z","signature_b64":"o3GuKiVbc2IneGtFC0W1O2T5ih+87E7+jTv9n1sigiQ+I9E72LkdDejlGSFf8jY2xM2B1YJOwQhAwpHMvqitCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4386d58ec7f382fa972ccca5d691d60e5a41ab02a9c655cfefb61f45c4d1b7a","last_reissued_at":"2026-05-17T23:45:22.324142Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:22.324142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerically Stable Polynomially Coded Computing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mohammad Fahim, Viveck R. Cadambe","submitted_at":"2019-03-20T03:24:53Z","abstract_excerpt":"We study the numerical stability of polynomial based encoding methods, which has emerged to be a powerful class of techniques for providing straggler and fault tolerance in the area of coded computing. Our contributions are as follows: 1) We construct new codes for matrix multiplication that achieve the same fault/straggler tolerance as the previously constructed MatDot Codes and Polynomial Codes. Unlike previous codes that use polynomials expanded in a monomial basis, our codes uses a basis of orthogonal polynomials. 2) We show that the condition number of every $m \\times m$ sub-matrix of an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08326","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":"1903.08326","created_at":"2026-05-17T23:45:22.324211+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.08326v2","created_at":"2026-05-17T23:45:22.324211+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08326","created_at":"2026-05-17T23:45:22.324211+00:00"},{"alias_kind":"pith_short_12","alias_value":"2Q4G2WHMP44C","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"2Q4G2WHMP44C7KLS","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"2Q4G2WHM","created_at":"2026-05-18T12:33:07.085635+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/2Q4G2WHMP44C7KLSZTFF22I5MD","json":"https://pith.science/pith/2Q4G2WHMP44C7KLSZTFF22I5MD.json","graph_json":"https://pith.science/api/pith-number/2Q4G2WHMP44C7KLSZTFF22I5MD/graph.json","events_json":"https://pith.science/api/pith-number/2Q4G2WHMP44C7KLSZTFF22I5MD/events.json","paper":"https://pith.science/paper/2Q4G2WHM"},"agent_actions":{"view_html":"https://pith.science/pith/2Q4G2WHMP44C7KLSZTFF22I5MD","download_json":"https://pith.science/pith/2Q4G2WHMP44C7KLSZTFF22I5MD.json","view_paper":"https://pith.science/paper/2Q4G2WHM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.08326&json=true","fetch_graph":"https://pith.science/api/pith-number/2Q4G2WHMP44C7KLSZTFF22I5MD/graph.json","fetch_events":"https://pith.science/api/pith-number/2Q4G2WHMP44C7KLSZTFF22I5MD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2Q4G2WHMP44C7KLSZTFF22I5MD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2Q4G2WHMP44C7KLSZTFF22I5MD/action/storage_attestation","attest_author":"https://pith.science/pith/2Q4G2WHMP44C7KLSZTFF22I5MD/action/author_attestation","sign_citation":"https://pith.science/pith/2Q4G2WHMP44C7KLSZTFF22I5MD/action/citation_signature","submit_replication":"https://pith.science/pith/2Q4G2WHMP44C7KLSZTFF22I5MD/action/replication_record"}},"created_at":"2026-05-17T23:45:22.324211+00:00","updated_at":"2026-05-17T23:45:22.324211+00:00"}