{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XWXJRXCYG34RAOYWPIQ2VGRC56","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":"62579b30612ebc5f0235e7ddbb8e4cbdbaf668df69530a0cfdeae71e4a002df1","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-04-08T17:38:17Z","title_canon_sha256":"7648bd50debfd11410abaf7fbc148e92a8b2c252be6b80e336a83c9437a53766"},"schema_version":"1.0","source":{"id":"1904.04216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04216","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04216v1","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04216","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"XWXJRXCYG34R","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XWXJRXCYG34RAOYW","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XWXJRXCY","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:b09fe41b6bf73136bddca2b2d863314fec9347e874906878939a9f8a2fe5e7f2","target":"graph","created_at":"2026-05-17T23:49:06Z","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":"The problem of tolerant junta testing is a natural and challenging problem which asks if the property of a function having some specified correlation with a $k$-Junta is testable. In this paper we give an affirmative answer to this question: We show that given distance parameters $\\frac{1}{2} >c_u>c_{\\ell} \\ge 0$, there is a tester which given oracle access to $f:\\{-1,1\\}^n \\rightarrow \\{-1,1\\}$, with query complexity $ 2^k \\cdot \\mathsf{poly}(k,1/|c_u-c_{\\ell}|)$ and distinguishes between the following cases:\n  $\\mathbf{1.}$ The distance of $f$ from any $k$-junta is at least $c_u$;\n  $\\mathbf","authors_text":"Anindya De, Elchanan Mossel, Joe Neeman","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-04-08T17:38:17Z","title":"Junta correlation is testable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04216","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":"sha256:1313c8818b5d10c8ca227a4484c1c22458343e20b6a5a97358f721f60eedab36","target":"record","created_at":"2026-05-17T23:49:06Z","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":"62579b30612ebc5f0235e7ddbb8e4cbdbaf668df69530a0cfdeae71e4a002df1","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-04-08T17:38:17Z","title_canon_sha256":"7648bd50debfd11410abaf7fbc148e92a8b2c252be6b80e336a83c9437a53766"},"schema_version":"1.0","source":{"id":"1904.04216","kind":"arxiv","version":1}},"canonical_sha256":"bdae98dc5836f9103b167a21aa9a22ef811f832a13ae033553f1d854bad7a38b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdae98dc5836f9103b167a21aa9a22ef811f832a13ae033553f1d854bad7a38b","first_computed_at":"2026-05-17T23:49:06.718805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:06.718805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jffIJXfiOtMhhtzToT6NqHYf6GbB75gsly55LeW8mlX462IPikp18EZSWCttuGbtBudA7zwWhgzwPjZqQmv+Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:06.719514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.04216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1313c8818b5d10c8ca227a4484c1c22458343e20b6a5a97358f721f60eedab36","sha256:b09fe41b6bf73136bddca2b2d863314fec9347e874906878939a9f8a2fe5e7f2"],"state_sha256":"e943d718a0224277ad76a1894585d88e2712af934477c0da2a944fac8acb6ae7"}