This manuscript illustration uses r=2, group names {0,1}, the interpolation interval {0,1}, and Q=R=2, outside the R<Q regime for the running-time bound. Four auxiliary labels are u0=(00,11), u1=(10,01), u2=(01,10), u12=(11,00), where each pair lists the sequences a,d. Put c=zeta_0-zeta_1-zeta_2+zeta_12. The row for u0 is P(T)zeta=zeta_0-(T/2)zeta_1-T*zeta_2. It restores zeta_0 at zero. At t=1 it equals c+(1/2)zeta_1-zeta_12; both remaining coordinates have a(1)=1, the assigned group. At t=2 it equals c-zeta_2-zeta_12; both have a(2)=1. Thus fixing c leaves only allowed local dependence at each point. This checks one row on a four-coordinate restriction, not the full construction or a speedup.