{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:455KFXFMXQSMHSJVUROL77WHXZ","short_pith_number":"pith:455KFXFM","schema_version":"1.0","canonical_sha256":"e77aa2dcacbc24c3c935a45cbffec7be611717b301f5f59fb76f919d26ecc4fc","source":{"kind":"arxiv","id":"0903.0566","version":2},"attestation_state":"computed","paper":{"title":"Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","quant-ph"],"primary_cat":"cs.IT","authors_text":"Gilles Zemor, Jean-Pierre Tillich","submitted_at":"2009-03-03T16:41:00Z","abstract_excerpt":"The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with fixed non-zero rate is logarithmic in the blocklength. We propose a construction of quantum LDPC codes with fixed non-zero rate and prove that the minimum distance grows proportionally to the square root of the blocklength."},"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":"0903.0566","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-03-03T16:41:00Z","cross_cats_sorted":["math.IT","quant-ph"],"title_canon_sha256":"6e4dda7a87a8173d77e383fbe4b42d68f9f780febb69fddcbcaed522a5bfd135","abstract_canon_sha256":"a0617dd9e8c96038624b5251f2085d6ca9ea956561256d7fbb990450e71b0d0e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:40.667532Z","signature_b64":"o4YukNjdFZ/KobcTN39Wk+li4nlxin8maLo6ifArQUCZw/OaRNGQUxDTbQlkxBcAGTkW17xH+mKNLYP2GxHsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e77aa2dcacbc24c3c935a45cbffec7be611717b301f5f59fb76f919d26ecc4fc","last_reissued_at":"2026-05-18T02:25:40.667068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:40.667068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","quant-ph"],"primary_cat":"cs.IT","authors_text":"Gilles Zemor, Jean-Pierre Tillich","submitted_at":"2009-03-03T16:41:00Z","abstract_excerpt":"The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with fixed non-zero rate is logarithmic in the blocklength. We propose a construction of quantum LDPC codes with fixed non-zero rate and prove that the minimum distance grows proportionally to the square root of the blocklength."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0566","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":"0903.0566","created_at":"2026-05-18T02:25:40.667154+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.0566v2","created_at":"2026-05-18T02:25:40.667154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.0566","created_at":"2026-05-18T02:25:40.667154+00:00"},{"alias_kind":"pith_short_12","alias_value":"455KFXFMXQSM","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"455KFXFMXQSMHSJV","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"455KFXFM","created_at":"2026-05-18T12:25:58.018023+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.08711","citing_title":"Coupled-Layer Construction of Quantum Product Codes","ref_index":26,"is_internal_anchor":true},{"citing_arxiv_id":"2604.27363","citing_title":"Constructing Bulk Topological Orders via Layered Gauging","ref_index":58,"is_internal_anchor":false},{"citing_arxiv_id":"2604.20013","citing_title":"Assessing System Capabilities and Bottlenecks of an Early Fault-Tolerant Bicycle Architecture","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2604.05126","citing_title":"In-Situ Simultaneous Magic State Injection on Arbitrary CSS qLDPC Codes","ref_index":49,"is_internal_anchor":false},{"citing_arxiv_id":"2604.18714","citing_title":"Efficient Routing of Quantum LDPC Codes on Programmable 2D Toric Architectures","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/455KFXFMXQSMHSJVUROL77WHXZ","json":"https://pith.science/pith/455KFXFMXQSMHSJVUROL77WHXZ.json","graph_json":"https://pith.science/api/pith-number/455KFXFMXQSMHSJVUROL77WHXZ/graph.json","events_json":"https://pith.science/api/pith-number/455KFXFMXQSMHSJVUROL77WHXZ/events.json","paper":"https://pith.science/paper/455KFXFM"},"agent_actions":{"view_html":"https://pith.science/pith/455KFXFMXQSMHSJVUROL77WHXZ","download_json":"https://pith.science/pith/455KFXFMXQSMHSJVUROL77WHXZ.json","view_paper":"https://pith.science/paper/455KFXFM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.0566&json=true","fetch_graph":"https://pith.science/api/pith-number/455KFXFMXQSMHSJVUROL77WHXZ/graph.json","fetch_events":"https://pith.science/api/pith-number/455KFXFMXQSMHSJVUROL77WHXZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/455KFXFMXQSMHSJVUROL77WHXZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/455KFXFMXQSMHSJVUROL77WHXZ/action/storage_attestation","attest_author":"https://pith.science/pith/455KFXFMXQSMHSJVUROL77WHXZ/action/author_attestation","sign_citation":"https://pith.science/pith/455KFXFMXQSMHSJVUROL77WHXZ/action/citation_signature","submit_replication":"https://pith.science/pith/455KFXFMXQSMHSJVUROL77WHXZ/action/replication_record"}},"created_at":"2026-05-18T02:25:40.667154+00:00","updated_at":"2026-05-18T02:25:40.667154+00:00"}