{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:UEPQWCTYXW2PCHXSD5DF4PQUXA","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":"7c2d03d3132d9610b1c4d9c3c2fb538f38b208fa24fc9ee51b8afa9ea4abc292","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"quant-ph","submitted_at":"1998-04-29T02:00:07Z","title_canon_sha256":"4512691d773ffdce224f845bab4aded11435f2b91df8756e10ca8e7ad128c728"},"schema_version":"1.0","source":{"id":"quant-ph/9804066","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9804066","created_at":"2026-07-04T14:47:11Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9804066v2","created_at":"2026-07-04T14:47:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9804066","created_at":"2026-07-04T14:47:11Z"},{"alias_kind":"pith_short_12","alias_value":"UEPQWCTYXW2P","created_at":"2026-07-04T14:47:11Z"},{"alias_kind":"pith_short_16","alias_value":"UEPQWCTYXW2PCHXS","created_at":"2026-07-04T14:47:11Z"},{"alias_kind":"pith_short_8","alias_value":"UEPQWCTY","created_at":"2026-07-04T14:47:11Z"}],"graph_snapshots":[{"event_id":"sha256:d1dc5d679aee5052eb27c5e203d127f621be9fff935f239c4843b776c25c91d4","target":"graph","created_at":"2026-07-04T14:47:11Z","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/quant-ph/9804066/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let X = (x_0,...,x_{n-1})$ be a sequence of n numbers. For \\epsilon > 0, we say that x_i is an \\epsilon-approximate median if the number of elements strictly less than x_i, and the number of elements strictly greater than x_i are each less than (1+\\epsilon)n/2. We consider the quantum query complexity of computing an \\epsilon-approximate median, given the sequence X as an oracle. We prove a lower bound of \\Omega(\\min{{1/\\epsilon},n}) queries for any quantum algorithm that computes an \\epsilon-approximate median with any constant probability greater than 1/2. We also show how an \\epsilon-approx","authors_text":"Ashwin Nayak, Felix Wu","cross_cats":["cs.CC"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1998-04-29T02:00:07Z","title":"The quantum query complexity of approximating the median and related statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9804066","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":"sha256:7618d87616f89fd1f3c9f2a11f9756baf5f9a5bb85705f813a65ad75b0f800a8","target":"record","created_at":"2026-07-04T14:47:11Z","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":"7c2d03d3132d9610b1c4d9c3c2fb538f38b208fa24fc9ee51b8afa9ea4abc292","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"quant-ph","submitted_at":"1998-04-29T02:00:07Z","title_canon_sha256":"4512691d773ffdce224f845bab4aded11435f2b91df8756e10ca8e7ad128c728"},"schema_version":"1.0","source":{"id":"quant-ph/9804066","kind":"arxiv","version":2}},"canonical_sha256":"a11f0b0a78bdb4f11ef21f465e3e14b80e3fbd439152e847b113386bd6e671ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a11f0b0a78bdb4f11ef21f465e3e14b80e3fbd439152e847b113386bd6e671ac","first_computed_at":"2026-07-04T14:47:11.912581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:47:11.912581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1IXMAaGTOy4jnu8HLdLAasqTM3vHKd9NgZa6lVb0GkF9UScHI/+RJ540doYbKhNl5kZrh7vbsc5v42BsVCwPCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:47:11.912951Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9804066","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7618d87616f89fd1f3c9f2a11f9756baf5f9a5bb85705f813a65ad75b0f800a8","sha256:d1dc5d679aee5052eb27c5e203d127f621be9fff935f239c4843b776c25c91d4"],"state_sha256":"4ab39ddf3e16db632ff133cc76664df64eb7ba29edaf817b573c8f5a8b779b03"}