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The lower bounds for 24 <= t <= 30 refute the conjecture that w(2;3,t) <= t^2, and we present an improved conjecture. We also investigate regularities in the good partitions (certificates) to better understand the lower bounds.\n  Motivated by such reglarities, we introduce *palindromic van der Waerden"},"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":"1102.5433","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-26T18:30:11Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"f2fc918eedb775993dac554cf755ca76fb9d1199e955b48fb85ec8ff82402677","abstract_canon_sha256":"9515dd0f4001086a77cf2748e18a5c09e1920b809732a740469025794f1763d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:00.387739Z","signature_b64":"M6nFLrQlkc5o+pLO1beKHtVZY6vzntRRZlWSdcxpwgAJl9TlgpVu7eK+UAb8gt190/0Tyx6IFgmT+qAhuVsMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc6433e0daec9d4e206978e4be3395dd093d593f9674349727e2149c1db33db1","last_reissued_at":"2026-05-18T01:41:00.387284Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:00.387284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the van der Waerden numbers w(2;3,t)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Hunter Snevily, Oliver Kullmann, Tanbir Ahmed","submitted_at":"2011-02-26T18:30:11Z","abstract_excerpt":"We present results and conjectures on the van der Waerden numbers w(2;3,t) and on the new palindromic van der Waerden numbers pdw(2;3,t). 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