{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5ECR3V7ETMGKD3QJ5WDXP6ZEM6","short_pith_number":"pith:5ECR3V7E","schema_version":"1.0","canonical_sha256":"e9051dd7e49b0ca1ee09ed8777fb24678fd0bba81327703dcbb5751b1d6e1eb2","source":{"kind":"arxiv","id":"1504.05653","version":1},"attestation_state":"computed","paper":{"title":"High rate locally-correctable and locally-testable codes with sub-polynomial query complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Noga Ron-Zewi, Or Meir, Shubhangi Saraf, Swastik Kopparty","submitted_at":"2015-04-22T04:52:50Z","abstract_excerpt":"In this work, we construct the first locally-correctable codes (LCCs), and locally-testable codes (LTCs) with constant rate, constant relative distance, and sub-polynomial query complexity. Specifically, we show that there exist binary LCCs and LTCs with block length $n$, constant rate (which can even be taken arbitrarily close to 1), constant relative distance, and query complexity $\\exp(\\tilde{O}(\\sqrt{\\log n}))$. Previously such codes were known to exist only with $\\Omega(n^{\\beta})$ query complexity (for constant $\\beta > 0$), and there were several, quite different, constructions known.\n "},"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":"1504.05653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-04-22T04:52:50Z","cross_cats_sorted":[],"title_canon_sha256":"d892dcc9436e807c811acce18503c039987bcafa79c5b3f5f0e9ad507061be83","abstract_canon_sha256":"d8cb5cae4c339cc54d43fa26488cad5bd6350ba97adb12abe42a317284d2adce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:13.057278Z","signature_b64":"FmoLmLycVOcrpGxgTwYZKf00/67MssimSzN5qSCFRCViyHKFdsTzIW7tzUcZkd6/e0SPz24zipgbFwwl2NqFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9051dd7e49b0ca1ee09ed8777fb24678fd0bba81327703dcbb5751b1d6e1eb2","last_reissued_at":"2026-05-18T02:18:13.056651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:13.056651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"High rate locally-correctable and locally-testable codes with sub-polynomial query complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Noga Ron-Zewi, Or Meir, Shubhangi Saraf, Swastik Kopparty","submitted_at":"2015-04-22T04:52:50Z","abstract_excerpt":"In this work, we construct the first locally-correctable codes (LCCs), and locally-testable codes (LTCs) with constant rate, constant relative distance, and sub-polynomial query complexity. Specifically, we show that there exist binary LCCs and LTCs with block length $n$, constant rate (which can even be taken arbitrarily close to 1), constant relative distance, and query complexity $\\exp(\\tilde{O}(\\sqrt{\\log n}))$. Previously such codes were known to exist only with $\\Omega(n^{\\beta})$ query complexity (for constant $\\beta > 0$), and there were several, quite different, constructions known.\n "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05653","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":"1504.05653","created_at":"2026-05-18T02:18:13.056743+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.05653v1","created_at":"2026-05-18T02:18:13.056743+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05653","created_at":"2026-05-18T02:18:13.056743+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ECR3V7ETMGK","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ECR3V7ETMGKD3QJ","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ECR3V7E","created_at":"2026-05-18T12:29:05.191682+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/5ECR3V7ETMGKD3QJ5WDXP6ZEM6","json":"https://pith.science/pith/5ECR3V7ETMGKD3QJ5WDXP6ZEM6.json","graph_json":"https://pith.science/api/pith-number/5ECR3V7ETMGKD3QJ5WDXP6ZEM6/graph.json","events_json":"https://pith.science/api/pith-number/5ECR3V7ETMGKD3QJ5WDXP6ZEM6/events.json","paper":"https://pith.science/paper/5ECR3V7E"},"agent_actions":{"view_html":"https://pith.science/pith/5ECR3V7ETMGKD3QJ5WDXP6ZEM6","download_json":"https://pith.science/pith/5ECR3V7ETMGKD3QJ5WDXP6ZEM6.json","view_paper":"https://pith.science/paper/5ECR3V7E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.05653&json=true","fetch_graph":"https://pith.science/api/pith-number/5ECR3V7ETMGKD3QJ5WDXP6ZEM6/graph.json","fetch_events":"https://pith.science/api/pith-number/5ECR3V7ETMGKD3QJ5WDXP6ZEM6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ECR3V7ETMGKD3QJ5WDXP6ZEM6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ECR3V7ETMGKD3QJ5WDXP6ZEM6/action/storage_attestation","attest_author":"https://pith.science/pith/5ECR3V7ETMGKD3QJ5WDXP6ZEM6/action/author_attestation","sign_citation":"https://pith.science/pith/5ECR3V7ETMGKD3QJ5WDXP6ZEM6/action/citation_signature","submit_replication":"https://pith.science/pith/5ECR3V7ETMGKD3QJ5WDXP6ZEM6/action/replication_record"}},"created_at":"2026-05-18T02:18:13.056743+00:00","updated_at":"2026-05-18T02:18:13.056743+00:00"}