Let E be a selected set of variable indices. To sum only assignments with x_i=1 for i in E, restrict each group fiber to local assignments meeting these requirements. Use representatives and local sums from these restricted fibers. Skip a measurement tuple if any restricted fiber is empty. The earlier separation condition still makes outside representatives interchangeable: restricting a set of permitted assignments does not invalidate that condition. For a+b=1, the fiber {(0,1),(1,0)} becomes {(1,0)} when E requires a=1. With E empty the original algorithm is recovered. This computes a restricted weighted sum, not necessarily a count.