# W(3,3)=27 certificate artifacts — SHA-256 (2026-07-21, incl. combined theorem)

c86cc8c8d24484f3a06baa47d5458d9a17a9a7098e090f11354eb49ec2e694b1  vdw_3_3_27.proof.json
c38782fab8f421e034206775b6345b123e09259ab0b0f1103efb091fc82f0b9d  lean_pkg/Vdw33Main.lean
aa057d92bdf00caf83b0f5a5fd4c1103d448ad4339f64058c88de9e0e60b29f7  lean_pkg/Vdw33Lower.lean
f99a3f7d82c762602e8f1e604bf3ac1d62ea355d22aefb306e11984b01b19edb  lean_pkg/Vdw33Combined.lean
0795bd0afad96710de2ca266169f7e1a01eb86f4d9e7c360fde29548df30889e  vdw_3_3_26.witness.json
5a2aa6988be34300aacab7de384ade47fa759c3215171188db20784528c7e925  RESULT.md

# aggregate over all .lean modules (sha256 of sorted per-file sha256 list):
a1b660ebe8924587d929585548c86e918c52c3ebbe78a08783062ae78c1035bc