{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BBJGJCAFCWR74OOTUZBXUICJXW","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":"c43de3ed86d033f6dab28a5a16ed7cd400d586e0a7df3fd07c9089a680dfe87c","cross_cats_sorted":["math.OC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-22T12:50:08Z","title_canon_sha256":"9f9873aca9da0e9214832dd1c1b621401ed3aecf24eb8848323557eed8dc0647"},"schema_version":"1.0","source":{"id":"1606.06930","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06930","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06930v2","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06930","created_at":"2026-05-18T00:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"BBJGJCAFCWR7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BBJGJCAFCWR74OOT","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BBJGJCAF","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:ca6591f1e752c104945ffd548dec9e25ac3a3ef6199dce5b8bcdf6559c3ab36c","target":"graph","created_at":"2026-05-18T00:19:42Z","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"},"paper":{"abstract_excerpt":"For nonnegative integers $n_2, n_3$ and $d$, let $N(n_2,n_3,d)$ denote the maximum cardinality of a code of length $n_2+n_3$, with $n_2$ binary coordinates and $n_3$ ternary coordinates (in this order) and with minimum distance at least $d$. For a nonnegative integer $k$, let $\\mathcal{C}_k$ denote the collection of codes of cardinality at most $k$. For $D \\in \\mathcal{C}_k$, define $S(D) := \\{C \\in \\mathcal{C}_k \\mid D \\subseteq C, |D| +2|C\\setminus D| \\leq k\\}$. Then $N(n_2,n_3,d)$ is upper bounded by the maximum value of $\\sum_{v \\in [2]^{n_2}[3]^{n_3}}x(\\{v\\})$, where $x$ is a function $\\m","authors_text":"Bart Litjens","cross_cats":["math.OC","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-22T12:50:08Z","title":"Semidefinite bounds for mixed binary/ternary codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06930","kind":"arxiv","version":2},"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":"sha256:3caaa2f344ec666c24a0ff456aae62135e996cd4d60387718fbe88bcae0bf86d","target":"record","created_at":"2026-05-18T00:19:42Z","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":"c43de3ed86d033f6dab28a5a16ed7cd400d586e0a7df3fd07c9089a680dfe87c","cross_cats_sorted":["math.OC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-22T12:50:08Z","title_canon_sha256":"9f9873aca9da0e9214832dd1c1b621401ed3aecf24eb8848323557eed8dc0647"},"schema_version":"1.0","source":{"id":"1606.06930","kind":"arxiv","version":2}},"canonical_sha256":"085264880515a3fe39d3a6437a2049bda6dc4fb46652e9f39d9b397e1ebc8659","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"085264880515a3fe39d3a6437a2049bda6dc4fb46652e9f39d9b397e1ebc8659","first_computed_at":"2026-05-18T00:19:42.767051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:42.767051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xObLmX+eDYK4QtTyT/tqb8op9ge/4iwnUL2z8BWP8av+e8v2B9BYwQa++0Xju9koNArf+GC6g+Cad3c2bfKZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:42.767700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06930","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3caaa2f344ec666c24a0ff456aae62135e996cd4d60387718fbe88bcae0bf86d","sha256:ca6591f1e752c104945ffd548dec9e25ac3a3ef6199dce5b8bcdf6559c3ab36c"],"state_sha256":"05c71a2fbb283656eedf1d4aaea6cee9fb08f386b4500311fe742e6fb4c59ea6"}