{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NLVCV2ID374SIUBIDWPHVODFTY","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":"ecf9cf0ac35924822e8bf70cf0c244763a7352eb29557c35ac3f426b4e3ea4d0","cross_cats_sorted":["cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-08-31T21:07:16Z","title_canon_sha256":"4453e47f2cf4ff92be6ea324deb95ab64bb7717800a12c80505226d25575a4c8"},"schema_version":"1.0","source":{"id":"1309.0157","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0157","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0157v2","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0157","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"NLVCV2ID374S","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NLVCV2ID374SIUBI","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NLVCV2ID","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:1eaded2ae6189d4bf2fe2e9fdbd54e16921f7348ddf320e778dc9a8c17eec63d","target":"graph","created_at":"2026-05-18T03:05:35Z","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":"We present a construction for complementary pairs of arrays that exploits a set of mutually-unbiased bases, and enumerate these arrays as well as the corresponding set of complementary sequences obtained from the arrays by projection. We also sketch an algorithm to uniquely generate these sequences. The pairwise squared inner-product of members of the sequence set is shown to be $\\frac{1}{2}$. Moreover, a subset of the set can be viewed as a codebook that asymptotically achieves $\\sqrt{\\frac{3}{2}}$ times the Welch bound.","authors_text":"Gaofei Wu, Matthew G. Parker","cross_cats":["cs.DM","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-08-31T21:07:16Z","title":"A complementary construction using mutually unbiased bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0157","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":"sha256:7177fb73863be76cd7d0a5f11377eca24e6adc6711cb02ef65f07882f910fbc8","target":"record","created_at":"2026-05-18T03:05:35Z","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":"ecf9cf0ac35924822e8bf70cf0c244763a7352eb29557c35ac3f426b4e3ea4d0","cross_cats_sorted":["cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-08-31T21:07:16Z","title_canon_sha256":"4453e47f2cf4ff92be6ea324deb95ab64bb7717800a12c80505226d25575a4c8"},"schema_version":"1.0","source":{"id":"1309.0157","kind":"arxiv","version":2}},"canonical_sha256":"6aea2ae903dff92450281d9e7ab8659e08312660b7e52e1ca366492fbbc384bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6aea2ae903dff92450281d9e7ab8659e08312660b7e52e1ca366492fbbc384bc","first_computed_at":"2026-05-18T03:05:35.400095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:35.400095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5oStW+b7YBBCoP0aN3FlLvXo+5UKWqYWSOuucmXquqf9ZgO9lkoKn1w3H/y7155QQ2NMa7DD4cD7RCV0SSMjCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:35.400526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0157","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7177fb73863be76cd7d0a5f11377eca24e6adc6711cb02ef65f07882f910fbc8","sha256:1eaded2ae6189d4bf2fe2e9fdbd54e16921f7348ddf320e778dc9a8c17eec63d"],"state_sha256":"3f3061adf2d69eba1d50a80ddc60d20f058ffbcce4e2e4a91efc46e8b8565f88"}