Process evaluation points, pairs (E,U), measurement tuples, and local assignments sequentially. Keep current indices, Boolean representatives, one group sum, one partial product, and an accumulator. Store the Q*J local coefficients needed for final interpolation, not a table for every assignment or tuple. Each polynomial list has only J coefficients on this rational-factor route. The layout arrays, current state, coefficient bit sizes, and exact interpolation workspace are polynomial in the stated parameters. Once D and the other parameters are polynomially bounded in the input size, this gives polynomial space. Polynomial space alone does not imply polynomial time.