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More specifically, we show the following:\n  $\\bullet$ If a boolean function $f$ can be expressed as a $t$-clipped decision tree, then under the action of a random $p$-restriction $\\rho$, the probability that the smallest depth decision tree for $f|_{\\rho}$ has depth greater than $d$ is upper bounded by $(4p2^{t})^{d}$.\n"},"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":"1703.00043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-02-28T20:28:03Z","cross_cats_sorted":[],"title_canon_sha256":"dadba4d45e88a3bbbc4bc57757f3ab3c979fcbe904bbf111a3349cca61f0976b","abstract_canon_sha256":"aeadf2ca39ae048d2246c45be5dd482885ad920465c777ae4696f3dad00ed5e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:46.162968Z","signature_b64":"zIpH9uLQXPEpLCB0WPdfLW+DUrNBG7TuBxmj1y2ADDEMmly1gSDN8ZIUuay2IytBDBUdHTSihhVJifY6IixWCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"278b092c56a6e46b31845768a2ab647628680fa98d7525862758d4071969b2b6","last_reissued_at":"2026-05-18T00:49:46.162463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:46.162463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tree tribes and lower bounds for switching lemmas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Jenish C. 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