Research log — W(2,7)

URLs actually opened.

• OEIS A005346, text format — exact values $1,3,9,35,178,1132$. $W(2,7)$ is not listed. Sequence last edited 2026-06-28.
• OEIS A005346 /list — Cloudflare interstitial; no extra terms.
• Wikipedia, Van der Waerden number — table still has $W(2,7)>3703$, citing Rabung–Lotts.
• Leaps in Bounds, $W(2,7)$ — lower bound recorded as $3704$ (i.e. a coloring of $3703$), update 2012-06-06.
• Herwig, Heule, van Lambalgen, van Maaren, E-JC 14 (2007) #R6 — cyclic zipper; $W(2,7)$ from prime $617$, $0$ zips, bound $>3703$.
• Heule PDF copy of the same paper
• Rabung and Lotts, E-JC 19(2) (2012) #P35 — faster zip check; primes to $10^7$; $W(2,7)$ not improved.
• Rabung–Lotts PDF
• DOI 10.37236/2363 — same paper via DOI.
• marijnheule/vdWaerden — SAT encoder and published certificates, including certificates/W_2_7_617.cert (3703 bytes). Used as a format/length check, not copied as a dent.
• Heule README
• Heule vdW-encode.c
• Heule check-cert.c
• Heule W_2_7_617.cert
• Erdős problems #138 — fetch timed out.
• Dransfield–Liu–Marek–Truszczyński SAT paper — early SAT lower bounds, not a $W(2,7)$ coloring of length $\ge 3704$.
• Kouril–Paul, $W(2,6)=1132$ — notes that the same preprocessing does not shrink $W(2,7)$.

No later accepted improvement of the $3703$ coloring was found in these sources.