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The proof for the 1-statement is based on the Hypergraph Container Method by Balogh, Morris and Samotij and Saxton and Thomason. The proof for the 0"},"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":"2006.05412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-06-09T17:21:26Z","cross_cats_sorted":[],"title_canon_sha256":"e717015561fca7cf7565453c2341c023eda3596226cb3331b845b90c29733454","abstract_canon_sha256":"d480d7b4398cce41c34bbdf849a16957aeaec56091923a1458e7469135cce8d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:56:53.131013Z","signature_b64":"vH7zCNv6I2JYc60any0Zo1eyxGnLPdG83GlnfMfR35bidUKN3U1HvV2Cby/Yqu2AewzoZiJ8y9jNXWfUzdkyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee4e3308ad192ecd42d2f4ca50979800104bf3bac10d458bb368364172e2b830","last_reissued_at":"2026-07-05T02:56:53.130591Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:56:53.130591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random Van der Waerden Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ohad Zohar","submitted_at":"2020-06-09T17:21:26Z","abstract_excerpt":"In this paper we prove the Random Van der Waerden Theorem: For $q_1 \\geq q_2 \\geq \\dotsb \\geq q_r \\geq 3 \\in \\mathbb{N}$ there exist $c,C >0$ such that \\[ \\lim_{n \\to \\infty} \\mathbb{P}([n]_p \\rightarrow (q_1,\\dotsc, q_r)) = \\begin{cases} 1 & \\text{if } p \\geq C \\cdot n^{-\\frac{q_2}{q_1(q_2-1)}}, 0 & \\text{if } p \\leq c \\cdot n^{-\\frac{q_2}{q_1(q_2-1)}}, \\end{cases}\\] extending the results of R\\\"odl and Ruci\\'nski for the symmetric case $q_i = q$. The proof for the 1-statement is based on the Hypergraph Container Method by Balogh, Morris and Samotij and Saxton and Thomason. 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