Succinct Rabung certificates and recurrence-closed lower bounds for van der Waerden numbers

We present three primitive three-colour Rabung certificates, giving nine direct lower bounds for van der Waerden numbers $W(3,k)$ with 17≤ k≤25. The five bounds for 17≤ k≤21 improve the earlier comparators in the explicit catalogue reviewed through 26 September 2026. In particular, $W(3,17)>31\,385\,622\,833$, a factor of $2.02$ above the identified predecessor. Each certificate is a triple $(p,r,k)$ describing a power-residue colouring. Multiplicative symmetry reduces its verification to a run-length test and a boundary condition. A GPU search finds candidate triples; a stand-alone CPU verifier reconstructs these finite hypotheses of Rabung's theorem. We prove the equivalence of the implemented boundary test with the published criterion and compare the resulting bounds with a finite closure of earlier constructions under known recurrences. Four earlier two-colour certificates are rechecked and credited to Monroe's distributed project. A separate empirical comparison of search intensities does not enter the lower-bound proof. The accompanying files include the manuscript, its LaTeX sources, and a reproducibility package containing code, certificate registries, archived execution evidence, and table generators. The manuscript, its LaTeX sources, and original data are licensed under CC BY 4.0; original code is licensed under the MIT licence. Third-party research objects are not redistributed.