q4 — fourth exact Parts rotation layer

This campaign adjoins a genuinely new fourth rotation layer to q3's entire combined graph. Starting from the 2,010-vertex union of the Parts graph, its 677-point reserve, and the first three rotation layers, it adds

Of the 509 source vertices, 85 already occur in the combined graph and 424 are new. build.py reconstructs those points exactly. It retains q3's already-replayed induced edges and compares every new point with every earlier point in exact arithmetic, thereby rebuilding every edge incident to the extension.

Search:

./run_search.sh

Full replay starts in the parent directory, where q1–q3 first verify the old induced graph and q4 then independently reconstructs the extension:

cd ..
./run_all.sh

Result

The exact graph has 2,434 vertices and 13,975 unit edges. The fourth layer contributes 424 new vertices and 2,209 edges incident to them. CaDiCaL found a proper five-coloring in 1.13 seconds, with color-class sizes 553, 430, 449, 522, and 480. The committed model passes the exact Python extension rebuild and the separate C edge/color checker.

This is residue, not a lower bound. The model restricts to every subgraph, so it covers arbitrary deletion of the 509 base vertices together with any subset of the 1,925 non-base vertices. It does not cover points beyond this reserve, deletion-and-replacement constructions using new coordinates, or another algebraic family.