{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HY5FOSB2OD4OWUP26SULCM65FH","short_pith_number":"pith:HY5FOSB2","schema_version":"1.0","canonical_sha256":"3e3a57483a70f8eb51faf4a8b133dd29c3e276e22f7a3f0f6549ac83123b1f81","source":{"kind":"arxiv","id":"1507.06175","version":2},"attestation_state":"computed","paper":{"title":"Efficient Low-Redundancy Codes for Correcting Multiple Deletions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS","math.IT"],"primary_cat":"cs.IT","authors_text":"Joshua Brakensiek, Samuel Zbarsky, Venkatesan Guruswami","submitted_at":"2015-07-22T13:20:28Z","abstract_excerpt":"We consider the problem of constructing binary codes to recover from $k$-bit deletions with efficient encoding/decoding, for a fixed $k$. The single deletion case is well understood, with the Varshamov-Tenengolts-Levenshtein code from 1965 giving an asymptotically optimal construction with $\\approx 2^n/n$ codewords of length $n$, i.e., at most $\\log n$ bits of redundancy. However, even for the case of two deletions, there was no known explicit construction with redundancy less than $n^{\\Omega(1)}$.\n  For any fixed $k$, we construct a binary code with $c_k \\log n$ redundancy that can be decoded"},"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":"1507.06175","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-07-22T13:20:28Z","cross_cats_sorted":["cs.DM","cs.DS","math.IT"],"title_canon_sha256":"5d8ca2246b1da59ebd2db8ee43a580f57c09d76c6de7cbb5b35d59b3ff66ff14","abstract_canon_sha256":"c094cb3a741b06e90b8dcc57d67475bf472fb7a8f99a25d053efeb0fe3d2aa98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:53.757287Z","signature_b64":"BhZUDk+FavZoqs9nwK/Zw/QfuZ6BwQOkB1YyTDSDwFx6jwibQ3cJNozAYRdjsgQJ8xjTfPdFw/C2Lquis9kDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e3a57483a70f8eb51faf4a8b133dd29c3e276e22f7a3f0f6549ac83123b1f81","last_reissued_at":"2026-05-17T23:45:53.756860Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:53.756860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient Low-Redundancy Codes for Correcting Multiple Deletions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS","math.IT"],"primary_cat":"cs.IT","authors_text":"Joshua Brakensiek, Samuel Zbarsky, Venkatesan Guruswami","submitted_at":"2015-07-22T13:20:28Z","abstract_excerpt":"We consider the problem of constructing binary codes to recover from $k$-bit deletions with efficient encoding/decoding, for a fixed $k$. The single deletion case is well understood, with the Varshamov-Tenengolts-Levenshtein code from 1965 giving an asymptotically optimal construction with $\\approx 2^n/n$ codewords of length $n$, i.e., at most $\\log n$ bits of redundancy. However, even for the case of two deletions, there was no known explicit construction with redundancy less than $n^{\\Omega(1)}$.\n  For any fixed $k$, we construct a binary code with $c_k \\log n$ redundancy that can be decoded"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06175","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":"1507.06175","created_at":"2026-05-17T23:45:53.756931+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.06175v2","created_at":"2026-05-17T23:45:53.756931+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06175","created_at":"2026-05-17T23:45:53.756931+00:00"},{"alias_kind":"pith_short_12","alias_value":"HY5FOSB2OD4O","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HY5FOSB2OD4OWUP2","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HY5FOSB2","created_at":"2026-05-18T12:29:25.134429+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/HY5FOSB2OD4OWUP26SULCM65FH","json":"https://pith.science/pith/HY5FOSB2OD4OWUP26SULCM65FH.json","graph_json":"https://pith.science/api/pith-number/HY5FOSB2OD4OWUP26SULCM65FH/graph.json","events_json":"https://pith.science/api/pith-number/HY5FOSB2OD4OWUP26SULCM65FH/events.json","paper":"https://pith.science/paper/HY5FOSB2"},"agent_actions":{"view_html":"https://pith.science/pith/HY5FOSB2OD4OWUP26SULCM65FH","download_json":"https://pith.science/pith/HY5FOSB2OD4OWUP26SULCM65FH.json","view_paper":"https://pith.science/paper/HY5FOSB2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.06175&json=true","fetch_graph":"https://pith.science/api/pith-number/HY5FOSB2OD4OWUP26SULCM65FH/graph.json","fetch_events":"https://pith.science/api/pith-number/HY5FOSB2OD4OWUP26SULCM65FH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HY5FOSB2OD4OWUP26SULCM65FH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HY5FOSB2OD4OWUP26SULCM65FH/action/storage_attestation","attest_author":"https://pith.science/pith/HY5FOSB2OD4OWUP26SULCM65FH/action/author_attestation","sign_citation":"https://pith.science/pith/HY5FOSB2OD4OWUP26SULCM65FH/action/citation_signature","submit_replication":"https://pith.science/pith/HY5FOSB2OD4OWUP26SULCM65FH/action/replication_record"}},"created_at":"2026-05-17T23:45:53.756931+00:00","updated_at":"2026-05-17T23:45:53.756931+00:00"}