{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:F75M5Q65HAHVTFK6QITOTYSMXO","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":"ceff3a1af5d04d102bfcbde111401a823545b22400dd2551489f82b8464b84c3","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-21T17:24:04Z","title_canon_sha256":"3875eb4c8cd366d1f77066f60e99adff3d4e8ca88f9ff9fdb789fb7dd5c1af0f"},"schema_version":"1.0","source":{"id":"1603.06505","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06505","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06505v6","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06505","created_at":"2026-05-18T00:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"F75M5Q65HAHV","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F75M5Q65HAHVTFK6","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F75M5Q65","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:3252d5bfe34236cd0d364152d5bbf7fc4a14b41904964c0cb293a58eeb886a6d","target":"graph","created_at":"2026-05-18T00:43:09Z","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 give and prove an optimal exact quantum query algorithm with complexity $k+1$ for computing the promise problem (i.e., symmetric and partial Boolean function) $DJ_n^k$ defined as: $DJ_n^k(x)=1$ for $|x|=n/2$, $DJ_n^k(x)=0$ for $|x|$ in the set $\\{0, 1,\\ldots, k, n-k, n-k+1,\\ldots,n\\}$, and it is undefined for the rest cases, where $n$ is even, $|x|$ is the Hamming weight of $x$. The case of $k=0$ is the well-known Deutsch-Jozsa problem. We outline all symmetric (and partial) Boolean functions with degrees 1 and 2, and prove their exact quantum query complexity. Then we prove that any symmet","authors_text":"Daowen Qiu, Shenggen Zheng","cross_cats":["cs.CC","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-21T17:24:04Z","title":"Characterizations of symmetrically partial Boolean functions with exact quantum query complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06505","kind":"arxiv","version":6},"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:b829ba18c6686c5045fee50488ed802d797d33d220d3aabfbc5a4c744373a260","target":"record","created_at":"2026-05-18T00:43:09Z","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":"ceff3a1af5d04d102bfcbde111401a823545b22400dd2551489f82b8464b84c3","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-21T17:24:04Z","title_canon_sha256":"3875eb4c8cd366d1f77066f60e99adff3d4e8ca88f9ff9fdb789fb7dd5c1af0f"},"schema_version":"1.0","source":{"id":"1603.06505","kind":"arxiv","version":6}},"canonical_sha256":"2ffacec3dd380f59955e8226e9e24cbba4154ab6c62ef02af4c122b08ea4442d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ffacec3dd380f59955e8226e9e24cbba4154ab6c62ef02af4c122b08ea4442d","first_computed_at":"2026-05-18T00:43:09.528299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:09.528299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vXXR6XiLLuWPEev30Xv94Qu80EyrXQXSek9WtZGofkWxEuvoRCXF7W0HFSYALKuHKffLSERDbT6UTHnr7mq9Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:09.529023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06505","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b829ba18c6686c5045fee50488ed802d797d33d220d3aabfbc5a4c744373a260","sha256:3252d5bfe34236cd0d364152d5bbf7fc4a14b41904964c0cb293a58eeb886a6d"],"state_sha256":"9db8edee9b07ed0ef50dfefd7dd37e5a3832c857282d535fa661b52adc74cadf"}