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In this work, we consider the problem of testing for $\\pi$-freeness with one-sided error, continuing the investigation of [Newman et al., SODA'17].\n  We demonstrate a surprising behavior for non-adaptive tests with one-sided error: While a trivial sampling-based approach yields an $\\varepsilon$-test for $\\pi$-freeness making $\\Theta(\\varepsilon^{-1/k} n^{1-1/k})"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.10660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-29T18:06:27Z","cross_cats_sorted":["cs.CC","math.CO"],"title_canon_sha256":"dbf4411071636500e4c5026702ad984e161a47448937391d93c1e73455bc7cf9","abstract_canon_sha256":"8360952f4ad20acdf5334e27dcb3b30157b23c60606031ecda862fbd2f933137"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:46.833187Z","signature_b64":"aAzT/QA/Y3BpKbV+jbQbaC9tV8iZHoJvZz1nl7weLEDbPo25/u30+99hzKNVmn4EOBLvgfQNbg2rYtWRGEQpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46f1860c28776d6337dca1fb6e4d5dfd701df030807ed9fce25d4143118d97a2","last_reissued_at":"2026-05-18T00:31:46.832690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:46.832690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved Bounds for Testing Forbidden Order Patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.CO"],"primary_cat":"cs.DS","authors_text":"Cl\\'ement L. 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