{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:F3T5UUQ352CVMGCE5P627LMSR7","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":"dd8d8f13ad7f0fbd82626a8cf0d2f938aee73a242090426683e2dd201b1dc10e","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-05-29T22:46:12Z","title_canon_sha256":"eefcc311588049a446f349889b8ab749b7c03b431abfcee118acf3145655a4dd"},"schema_version":"1.0","source":{"id":"1605.09071","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09071","created_at":"2026-05-18T00:55:57Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09071v2","created_at":"2026-05-18T00:55:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09071","created_at":"2026-05-18T00:55:57Z"},{"alias_kind":"pith_short_12","alias_value":"F3T5UUQ352CV","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"F3T5UUQ352CVMGCE","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"F3T5UUQ3","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:f72d43a275562012245d8e9b418129ff5e5090fb4bfb9684122132c75e3e4123","target":"graph","created_at":"2026-05-18T00:55:57Z","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 study the composition question for bounded-error randomized query complexity: Is R(f o g) = Omega(R(f) R(g)) for all Boolean functions f and g? We show that inserting a simple Boolean function h, whose query complexity is only Theta(log R(g)), in between f and g allows us to prove R(f o h o g) = Omega(R(f) R(h) R(g)).\n  We prove this using a new lower bound measure for randomized query complexity we call randomized sabotage complexity, RS(f). Randomized sabotage complexity has several desirable properties, such as a perfect composition theorem, RS(f o g) >= RS(f) RS(g), and a composition th","authors_text":"Robin Kothari, Shalev Ben-David","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-05-29T22:46:12Z","title":"Randomized query complexity of sabotaged and composed functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09071","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":"sha256:5fa66a4fb64c2ca437970cefb7787a53882617ced61379723536182411a19b1e","target":"record","created_at":"2026-05-18T00:55:57Z","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":"dd8d8f13ad7f0fbd82626a8cf0d2f938aee73a242090426683e2dd201b1dc10e","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-05-29T22:46:12Z","title_canon_sha256":"eefcc311588049a446f349889b8ab749b7c03b431abfcee118acf3145655a4dd"},"schema_version":"1.0","source":{"id":"1605.09071","kind":"arxiv","version":2}},"canonical_sha256":"2ee7da521bee85561844ebfdafad928fc20e7debcb0dcc16a88f7bbf5add345d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ee7da521bee85561844ebfdafad928fc20e7debcb0dcc16a88f7bbf5add345d","first_computed_at":"2026-05-18T00:55:57.948628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:57.948628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pbKWtucmOjWCE3GvvaTXedAECyRuy6B+ivb9k8HPzC3auEt+R4ckAgdqwYmHOh0uS+zttZfc9Gsjc4DGXBtTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:57.949201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.09071","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fa66a4fb64c2ca437970cefb7787a53882617ced61379723536182411a19b1e","sha256:f72d43a275562012245d8e9b418129ff5e5090fb4bfb9684122132c75e3e4123"],"state_sha256":"e4c3783a0b67629935124f326bf24115cfccb42a8e6c94aa3dcd250cda4bb85f"}