{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:X2MHB4NIABO7IYAUIFUYO7GQZY","short_pith_number":"pith:X2MHB4NI","schema_version":"1.0","canonical_sha256":"be9870f1a8005df460144169877cd0ce30fe462b6859d99874640001727fdc1b","source":{"kind":"arxiv","id":"2203.06568","version":4},"attestation_state":"computed","paper":{"title":"Semidefinite programming bounds for binary codes from a split Terwilliger algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Ching-Yi Lai, Pin-Chieh Tseng, Wei-Hsuan Yu","submitted_at":"2022-03-13T05:01:37Z","abstract_excerpt":"We study the upper bounds for $A(n,d)$, the maximum size of codewords with length $n$ and Hamming distance at least $d$. Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to bound $A(n, d)$. We derive more sophisticated matrix inequalities based on a split Terwilliger algebra to improve Schrijver's semidefinite programming bounds on $A(n, d)$. In particular, we improve the semidefinite programming bounds on $A(18,4)$ to $6551$."},"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":"2203.06568","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-03-13T05:01:37Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"bd491aa69d9c0242d7746a09cc716c15b54ff6afebd236540b4d4f89e875a0b8","abstract_canon_sha256":"fdb3b4d68b0d1e3efdc21dfd2f25bf81209e67295373608a6ea5b2d86e936659"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:19:15.299975Z","signature_b64":"HfsaUAEm3B5+UJWCCuNNgZL8jDbOVJTLLU/i6fOWJmGP5FLhNCJWxxxdyqnQz0GQdY9JAjAtFJbfc93FOtzxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be9870f1a8005df460144169877cd0ce30fe462b6859d99874640001727fdc1b","last_reissued_at":"2026-07-05T06:19:15.299482Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:19:15.299482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semidefinite programming bounds for binary codes from a split Terwilliger algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Ching-Yi Lai, Pin-Chieh Tseng, Wei-Hsuan Yu","submitted_at":"2022-03-13T05:01:37Z","abstract_excerpt":"We study the upper bounds for $A(n,d)$, the maximum size of codewords with length $n$ and Hamming distance at least $d$. Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to bound $A(n, d)$. We derive more sophisticated matrix inequalities based on a split Terwilliger algebra to improve Schrijver's semidefinite programming bounds on $A(n, d)$. In particular, we improve the semidefinite programming bounds on $A(18,4)$ to $6551$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.06568","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.06568/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2203.06568","created_at":"2026-07-05T06:19:15.299542+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.06568v4","created_at":"2026-07-05T06:19:15.299542+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.06568","created_at":"2026-07-05T06:19:15.299542+00:00"},{"alias_kind":"pith_short_12","alias_value":"X2MHB4NIABO7","created_at":"2026-07-05T06:19:15.299542+00:00"},{"alias_kind":"pith_short_16","alias_value":"X2MHB4NIABO7IYAU","created_at":"2026-07-05T06:19:15.299542+00:00"},{"alias_kind":"pith_short_8","alias_value":"X2MHB4NI","created_at":"2026-07-05T06:19:15.299542+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/X2MHB4NIABO7IYAUIFUYO7GQZY","json":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY.json","graph_json":"https://pith.science/api/pith-number/X2MHB4NIABO7IYAUIFUYO7GQZY/graph.json","events_json":"https://pith.science/api/pith-number/X2MHB4NIABO7IYAUIFUYO7GQZY/events.json","paper":"https://pith.science/paper/X2MHB4NI"},"agent_actions":{"view_html":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY","download_json":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY.json","view_paper":"https://pith.science/paper/X2MHB4NI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.06568&json=true","fetch_graph":"https://pith.science/api/pith-number/X2MHB4NIABO7IYAUIFUYO7GQZY/graph.json","fetch_events":"https://pith.science/api/pith-number/X2MHB4NIABO7IYAUIFUYO7GQZY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY/action/storage_attestation","attest_author":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY/action/author_attestation","sign_citation":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY/action/citation_signature","submit_replication":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY/action/replication_record"}},"created_at":"2026-07-05T06:19:15.299542+00:00","updated_at":"2026-07-05T06:19:15.299542+00:00"}