{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:X2MHB4NIABO7IYAUIFUYO7GQZY","short_pith_number":"pith:X2MHB4NI","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"},"canonical_sha256":"be9870f1a8005df460144169877cd0ce30fe462b6859d99874640001727fdc1b","source":{"kind":"arxiv","id":"2203.06568","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.06568","created_at":"2026-07-05T06:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"2203.06568v4","created_at":"2026-07-05T06:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.06568","created_at":"2026-07-05T06:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"X2MHB4NIABO7","created_at":"2026-07-05T06:19:15Z"},{"alias_kind":"pith_short_16","alias_value":"X2MHB4NIABO7IYAU","created_at":"2026-07-05T06:19:15Z"},{"alias_kind":"pith_short_8","alias_value":"X2MHB4NI","created_at":"2026-07-05T06:19:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:X2MHB4NIABO7IYAUIFUYO7GQZY","target":"record","payload":{"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"},"canonical_sha256":"be9870f1a8005df460144169877cd0ce30fe462b6859d99874640001727fdc1b","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"},"source_kind":"arxiv","source_id":"2203.06568","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:19:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TIBPSWUQfc3sCF3bWmWXA8ij2QMNPll0dMgomqZD+38b9Pf+ZV8gMJ1n6tB+ixojxXNLX2HJs6N4ZbpgkNUTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T15:09:53.590917Z"},"content_sha256":"582e0255ab3682c9889657d9e214aba186cdf762634bd93fdf71dcb344306c02","schema_version":"1.0","event_id":"sha256:582e0255ab3682c9889657d9e214aba186cdf762634bd93fdf71dcb344306c02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:X2MHB4NIABO7IYAUIFUYO7GQZY","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:19:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vw+e91T6CCQlpmmkvNAk0j86wMvLgaNXvmVnisl7i5nQ0hkCgzY5OuXVij2zEe5wMNNX1fjSLFkJeO/mo4y8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T15:09:53.591229Z"},"content_sha256":"fa9fa057a5d6a6492c6888927ae57bfe1ca11b6de1d0079de38db1a646439ebf","schema_version":"1.0","event_id":"sha256:fa9fa057a5d6a6492c6888927ae57bfe1ca11b6de1d0079de38db1a646439ebf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY/bundle.json","state_url":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X2MHB4NIABO7IYAUIFUYO7GQZY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-17T15:09:53Z","links":{"resolver":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY","bundle":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY/bundle.json","state":"https://pith.science/pith/X2MHB4NIABO7IYAUIFUYO7GQZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X2MHB4NIABO7IYAUIFUYO7GQZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:X2MHB4NIABO7IYAUIFUYO7GQZY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fdb3b4d68b0d1e3efdc21dfd2f25bf81209e67295373608a6ea5b2d86e936659","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-03-13T05:01:37Z","title_canon_sha256":"bd491aa69d9c0242d7746a09cc716c15b54ff6afebd236540b4d4f89e875a0b8"},"schema_version":"1.0","source":{"id":"2203.06568","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.06568","created_at":"2026-07-05T06:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"2203.06568v4","created_at":"2026-07-05T06:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.06568","created_at":"2026-07-05T06:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"X2MHB4NIABO7","created_at":"2026-07-05T06:19:15Z"},{"alias_kind":"pith_short_16","alias_value":"X2MHB4NIABO7IYAU","created_at":"2026-07-05T06:19:15Z"},{"alias_kind":"pith_short_8","alias_value":"X2MHB4NI","created_at":"2026-07-05T06:19:15Z"}],"graph_snapshots":[{"event_id":"sha256:fa9fa057a5d6a6492c6888927ae57bfe1ca11b6de1d0079de38db1a646439ebf","target":"graph","created_at":"2026-07-05T06:19:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.06568/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 $6551$.","authors_text":"Ching-Yi Lai, Pin-Chieh Tseng, Wei-Hsuan Yu","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-03-13T05:01:37Z","title":"Semidefinite programming bounds for binary codes from a split Terwilliger algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.06568","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:582e0255ab3682c9889657d9e214aba186cdf762634bd93fdf71dcb344306c02","target":"record","created_at":"2026-07-05T06:19:15Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fdb3b4d68b0d1e3efdc21dfd2f25bf81209e67295373608a6ea5b2d86e936659","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2022-03-13T05:01:37Z","title_canon_sha256":"bd491aa69d9c0242d7746a09cc716c15b54ff6afebd236540b4d4f89e875a0b8"},"schema_version":"1.0","source":{"id":"2203.06568","kind":"arxiv","version":4}},"canonical_sha256":"be9870f1a8005df460144169877cd0ce30fe462b6859d99874640001727fdc1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be9870f1a8005df460144169877cd0ce30fe462b6859d99874640001727fdc1b","first_computed_at":"2026-07-05T06:19:15.299482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:19:15.299482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HfsaUAEm3B5+UJWCCuNNgZL8jDbOVJTLLU/i6fOWJmGP5FLhNCJWxxxdyqnQz0GQdY9JAjAtFJbfc93FOtzxDA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:19:15.299975Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.06568","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:582e0255ab3682c9889657d9e214aba186cdf762634bd93fdf71dcb344306c02","sha256:fa9fa057a5d6a6492c6888927ae57bfe1ca11b6de1d0079de38db1a646439ebf"],"state_sha256":"eea73a6b71556ad3a750cd219f98fe111493e704838791116ee1bde46880e59f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gs7FO6NhwZ/m6jWcRKm4mMox1cndgDYiSRbrwJG2+AbDNHObzisQt6D++zyo6GP13RSzjOpvoRZhXcEujE0+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T15:09:53.594368Z","bundle_sha256":"8edfa7d82674f091fabd2c28f7524c74686c2d45887b964238cbbf7572a8137b"}}