{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:B3VMS2GJG4DRYQTNUNEXD6JU7X","short_pith_number":"pith:B3VMS2GJ","schema_version":"1.0","canonical_sha256":"0eeac968c937071c426da34971f934fddbab3fddf5e78fdbac1dbeac75b4984c","source":{"kind":"arxiv","id":"0910.5301","version":3},"attestation_state":"computed","paper":{"title":"Using Elimination Theory to construct Rigid Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.CC","authors_text":"Abhinav Kumar, Jayalal Sarma M. N, Satyanarayana V. Lokam, Vijay M. Patankar","submitted_at":"2009-10-28T07:56:23Z","abstract_excerpt":"The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant (1977), rigidity and similar rank-robustness functions of matrices have found numerous applications in circuit complexity, communication complexity, and learning complexity. Almost all nxn matrices over an infinite field have a rigidity of (n-r)^2. It is a long-standing open question to construct infinite families of explicit matrices even with superlinear rigidity when r = Omega(n).\n  In this paper"},"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":"0910.5301","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2009-10-28T07:56:23Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ef5a220700ea2124ae9d30a7bfa99ac66bafa9d1d431c1d6ae633e3e5207b2d7","abstract_canon_sha256":"dd1bfbab4b8175b01dd21ca121c3c2e1ec558aed569a2d688224ce98f814889b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:48.635149Z","signature_b64":"PQNYNspnxUSKDSQUsPIjroNn+KgDOd2B3b6l4Yx2zaNHTs+MOu0biC18yhD/0acMPO8HG0QX761g3LwGpPdXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0eeac968c937071c426da34971f934fddbab3fddf5e78fdbac1dbeac75b4984c","last_reissued_at":"2026-05-18T02:28:48.634691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:48.634691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Using Elimination Theory to construct Rigid Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.CC","authors_text":"Abhinav Kumar, Jayalal Sarma M. N, Satyanarayana V. Lokam, Vijay M. Patankar","submitted_at":"2009-10-28T07:56:23Z","abstract_excerpt":"The rigidity of a matrix A for target rank r is the minimum number of entries of A that must be changed to ensure that the rank of the altered matrix is at most r. Since its introduction by Valiant (1977), rigidity and similar rank-robustness functions of matrices have found numerous applications in circuit complexity, communication complexity, and learning complexity. Almost all nxn matrices over an infinite field have a rigidity of (n-r)^2. It is a long-standing open question to construct infinite families of explicit matrices even with superlinear rigidity when r = Omega(n).\n  In this paper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.5301","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":""},"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":"0910.5301","created_at":"2026-05-18T02:28:48.634784+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.5301v3","created_at":"2026-05-18T02:28:48.634784+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.5301","created_at":"2026-05-18T02:28:48.634784+00:00"},{"alias_kind":"pith_short_12","alias_value":"B3VMS2GJG4DR","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"B3VMS2GJG4DRYQTN","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"B3VMS2GJ","created_at":"2026-05-18T12:25:58.837520+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/B3VMS2GJG4DRYQTNUNEXD6JU7X","json":"https://pith.science/pith/B3VMS2GJG4DRYQTNUNEXD6JU7X.json","graph_json":"https://pith.science/api/pith-number/B3VMS2GJG4DRYQTNUNEXD6JU7X/graph.json","events_json":"https://pith.science/api/pith-number/B3VMS2GJG4DRYQTNUNEXD6JU7X/events.json","paper":"https://pith.science/paper/B3VMS2GJ"},"agent_actions":{"view_html":"https://pith.science/pith/B3VMS2GJG4DRYQTNUNEXD6JU7X","download_json":"https://pith.science/pith/B3VMS2GJG4DRYQTNUNEXD6JU7X.json","view_paper":"https://pith.science/paper/B3VMS2GJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.5301&json=true","fetch_graph":"https://pith.science/api/pith-number/B3VMS2GJG4DRYQTNUNEXD6JU7X/graph.json","fetch_events":"https://pith.science/api/pith-number/B3VMS2GJG4DRYQTNUNEXD6JU7X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B3VMS2GJG4DRYQTNUNEXD6JU7X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B3VMS2GJG4DRYQTNUNEXD6JU7X/action/storage_attestation","attest_author":"https://pith.science/pith/B3VMS2GJG4DRYQTNUNEXD6JU7X/action/author_attestation","sign_citation":"https://pith.science/pith/B3VMS2GJG4DRYQTNUNEXD6JU7X/action/citation_signature","submit_replication":"https://pith.science/pith/B3VMS2GJG4DRYQTNUNEXD6JU7X/action/replication_record"}},"created_at":"2026-05-18T02:28:48.634784+00:00","updated_at":"2026-05-18T02:28:48.634784+00:00"}