Succinct Rabung certificates and recurrence-closed lower bounds for van der Waerden numbers
Rabung's power-residue construction describes a large progression-free colouring by a prime, a colour count and a target length. We give six additional primitive certificates, checked by full ordinary CPU scans, which yield fourteen direct lower bounds. In colour-first notation, these include $W(3,17)>33\,166\,190\,897$, $W(3,18)>100\,289\,348\,022$, $W(3,19)>259\,446\,988\,783$ and $W(3,20)>326\,368\,775\,450$. The larger ternary primes lie outside the complete census below $2^{32}$. We prove the equivalence of the run and boundary tests with Rabung's criterion and separate pointwise…
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