{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:KXF7Y7G4ZT5MMJQEYY7RX3CHNH","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":"66ecc04813371caf31656916daaba2a1594b69aa7905796f03255ee6404f6dea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-07-10T19:29:52Z","title_canon_sha256":"636814acdcf67d5e18b2aa3afefb28284a74475f91ee6c2f66cc4114c396ef8f"},"schema_version":"1.0","source":{"id":"2007.05580","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.05580","created_at":"2026-07-05T01:20:20Z"},{"alias_kind":"arxiv_version","alias_value":"2007.05580v2","created_at":"2026-07-05T01:20:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.05580","created_at":"2026-07-05T01:20:20Z"},{"alias_kind":"pith_short_12","alias_value":"KXF7Y7G4ZT5M","created_at":"2026-07-05T01:20:20Z"},{"alias_kind":"pith_short_16","alias_value":"KXF7Y7G4ZT5MMJQE","created_at":"2026-07-05T01:20:20Z"},{"alias_kind":"pith_short_8","alias_value":"KXF7Y7G4","created_at":"2026-07-05T01:20:20Z"}],"graph_snapshots":[{"event_id":"sha256:0059f52e544c63e4a1f65e457fa371dcef1daf8ab5c1bad933746267fe7791ce","target":"graph","created_at":"2026-07-05T01:20:20Z","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/2007.05580/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a strong direct sum theorem for computing $xor \\circ g$. Specifically, we show that for every function g and every $k\\geq 2$, the randomized query complexity of computing the xor of k instances of g satisfies $\\overline{R}_\\eps(xor\\circ g) = \\Theta(k \\overline{R}_{\\eps/k}(g))$. This matches the naive success amplification upper bound and answers a conjecture of Blais and Brody (CCC19).\n  As a consequence of our strong direct sum theorem, we give a total function g for which $R(xor \\circ g) = \\Theta(k \\log(k)\\cdot R(g))$, answering an open question from Ben-David et al.(arxiv:2006.10957","authors_text":"Hariharan Srinivasulu, Jae Tak Kim, Joshua Brody, Peem Lerdputtipongporn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-07-10T19:29:52Z","title":"A Strong XOR Lemma for Randomized Query Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.05580","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":"sha256:8fc9e3b6c46323428dd136145966c6b27a6fbaf3d3e0d689ef1a9384944d72b5","target":"record","created_at":"2026-07-05T01:20:20Z","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":"66ecc04813371caf31656916daaba2a1594b69aa7905796f03255ee6404f6dea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-07-10T19:29:52Z","title_canon_sha256":"636814acdcf67d5e18b2aa3afefb28284a74475f91ee6c2f66cc4114c396ef8f"},"schema_version":"1.0","source":{"id":"2007.05580","kind":"arxiv","version":2}},"canonical_sha256":"55cbfc7cdcccfac62604c63f1bec4769ec35bc7ed5f31b2dcc1a0bdba7130a47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55cbfc7cdcccfac62604c63f1bec4769ec35bc7ed5f31b2dcc1a0bdba7130a47","first_computed_at":"2026-07-05T01:20:20.310430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:20:20.310430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RNczHy0gulQXxyj8z2R2my4Jby/1TNChjUmx/3mAq2KWTxvMtXbiF/9dN3eGId+5AeqxDY/XWmjAV+FVm4CrCA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:20:20.310878Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.05580","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fc9e3b6c46323428dd136145966c6b27a6fbaf3d3e0d689ef1a9384944d72b5","sha256:0059f52e544c63e4a1f65e457fa371dcef1daf8ab5c1bad933746267fe7791ce"],"state_sha256":"902e3b2e02cd9232293fae303dc24fc448e36334e8a3ae2226ee55da4b6e4e2d"}