Hamilton-cycle weak saturation in a two-parameter family of grids

We prove wsat(P_R square P_n, C_(Rn)) = Rn+3 for every even R >= 26 and every odd n >= 15, with the two dimensions varying independently; the result also applies to isomorphic transposes. A finite Hamilton restoration order in a 26 by 15 grid supplies the base. Nineteen exact column-word transitions enlarge its width, while compatible row-word transitions enlarge its height. Complementary edge indicators preserve spanning path matchings where the insertion directions cross, including newly created ports; decorated graph words establish availability at every stage. Four face-coordinate constraints give the matching lower bound. The construction provides a connected, initially Hamilton-free optimal seed. The ordered restoration witnesses form an explicit basis of the binary Hamilton-cycle span of size (R-1)(n-1)-4. The dimension formula also follows from Yan's earlier signing characterization. The supporting record contains exact finite inputs, the kernel-checked concrete finite contract and universal construction, and complementary independently written exact checkers.