{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HOB5URA7ZAINQ2QL2CMVXPFQLR","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":"a9611fae1daf9742b11fa6f3f48ee0701e2bbd049b0e5f9c47da71690c455a01","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-09-29T10:00:34Z","title_canon_sha256":"e3ff5d8da5bd85207c42935a0ef68e08e99b809714484b3fa90db64c3e78e132"},"schema_version":"1.0","source":{"id":"1309.7565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7565","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7565v1","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7565","created_at":"2026-05-18T03:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"HOB5URA7ZAIN","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HOB5URA7ZAINQ2QL","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HOB5URA7","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:2689167c46e224e72e3ff3952c8628e201db7712909e000ffa6dc06154a727d1","target":"graph","created_at":"2026-05-18T03:11:56Z","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 consider the randomized decision tree complexity of the recursive 3-majority function. We prove a lower bound of $(1/2-\\delta) \\cdot 2.57143^h$ for the two-sided-error randomized decision tree complexity of evaluating height $h$ formulae with error $\\delta \\in [0,1/2)$. This improves the lower bound of $(1-2\\delta)(7/3)^h$ given by Jayram, Kumar, and Sivakumar (STOC'03), and the one of $(1-2\\delta) \\cdot 2.55^h$ given by Leonardos (ICALP'13). Second, we improve the upper bound by giving a new zero-error randomized decision tree algorithm that has complexity at most $(1.007) \\cdot 2.64944^h$","authors_text":"Ashwin Nayak, David Xiao, Frederic Magniez, Gabor Tardos, Jonah Sherman, Miklos Santha","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-09-29T10:00:34Z","title":"Improved bounds for the randomized decision tree complexity of recursive majority"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7565","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":"sha256:9faa170b9e09d0389c5471e1c4ac08f0ea096fb1325af625f2a80dd83e3f3dd9","target":"record","created_at":"2026-05-18T03:11:56Z","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":"a9611fae1daf9742b11fa6f3f48ee0701e2bbd049b0e5f9c47da71690c455a01","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-09-29T10:00:34Z","title_canon_sha256":"e3ff5d8da5bd85207c42935a0ef68e08e99b809714484b3fa90db64c3e78e132"},"schema_version":"1.0","source":{"id":"1309.7565","kind":"arxiv","version":1}},"canonical_sha256":"3b83da441fc810d86a0bd0995bbcb05c42e05f0daa2bf8a1cf34599c11438c26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b83da441fc810d86a0bd0995bbcb05c42e05f0daa2bf8a1cf34599c11438c26","first_computed_at":"2026-05-18T03:11:56.553917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:56.553917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"maQSgl5j1DzycFPUT4xuRDWiM71sg0oF4lqtGyG1J1yyYAwrTQfEDkjimKc9J6Yi+pgtnlAQgIh8cdIZ/iCCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:56.554781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9faa170b9e09d0389c5471e1c4ac08f0ea096fb1325af625f2a80dd83e3f3dd9","sha256:2689167c46e224e72e3ff3952c8628e201db7712909e000ffa6dc06154a727d1"],"state_sha256":"b66595aa071c5bb1b28e2cbbd8940f38e62c812639ec2bf75772a7d0839b02a3"}