{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:EVWA6GXWKSCXGPZZAENWBX4SHW","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":"f660b428d69acbe7b76582abe5af6fec92d647521fd7e3b074cb94011e0086bd","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"math.PR","submitted_at":"2004-10-12T00:09:35Z","title_canon_sha256":"821f62843efdee7a9434cbbd1272d76db322bcac48b8cd005ec80b7d72742c6d"},"schema_version":"1.0","source":{"id":"math/0410282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0410282","created_at":"2026-05-18T03:53:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0410282v1","created_at":"2026-05-18T03:53:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0410282","created_at":"2026-05-18T03:53:05Z"},{"alias_kind":"pith_short_12","alias_value":"EVWA6GXWKSCX","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"EVWA6GXWKSCXGPZZ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"EVWA6GXW","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:06d77a5bc3a6fbbdc2520db115df38d6fe25c0c6e6b38ea5682d23f7cb4ce795","target":"graph","created_at":"2026-05-18T03:53:05Z","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":"A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random inputs, no input bit is read with probability more than Theta(n^{-1/2} sqrt{log n}). We give a balanced monotone Boolean function for which the corresponding probability is Theta(n^{-1/3} log n). We then show that for any randomized algorithm for evaluating a balanced Boolean function, when the input bits are uniformly random, there is some input bit that is read ","authors_text":"David B. Wilson, Itai Benjamini, Oded Schramm","cross_cats":["cs.CC"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2004-10-12T00:09:35Z","title":"Balanced Boolean functions that can be evaluated so that every input bit is unlikely to be read"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410282","kind":"arxiv","version":1},"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":"sha256:634afacd45e868a266240000a4013cd2f17b66aa5f7d38c7a2173d63030c6892","target":"record","created_at":"2026-05-18T03:53:05Z","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":"f660b428d69acbe7b76582abe5af6fec92d647521fd7e3b074cb94011e0086bd","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"math.PR","submitted_at":"2004-10-12T00:09:35Z","title_canon_sha256":"821f62843efdee7a9434cbbd1272d76db322bcac48b8cd005ec80b7d72742c6d"},"schema_version":"1.0","source":{"id":"math/0410282","kind":"arxiv","version":1}},"canonical_sha256":"256c0f1af65485733f39011b60df923d81fbe0fb51e453b39e9d2615a23050c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"256c0f1af65485733f39011b60df923d81fbe0fb51e453b39e9d2615a23050c6","first_computed_at":"2026-05-18T03:53:05.282083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:05.282083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KD5OTtR5v1o1yGF6N68xIU+0Fd6eLVQTqBGY7myQvwQoXPVvZK7M2gC4lKHhqhUC8173PSSUyX9I9IKPMkDJAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:05.282741Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0410282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:634afacd45e868a266240000a4013cd2f17b66aa5f7d38c7a2173d63030c6892","sha256:06d77a5bc3a6fbbdc2520db115df38d6fe25c0c6e6b38ea5682d23f7cb4ce795"],"state_sha256":"c53e4f4fbf6585cf3051565687dc30683bd7415bc21243f9c83e80d269f00d1e"}