  which gives a unique value for z in the generic case. But looking at the space of all possible dynamics for this lattice (i.e., the space of all possible weighting factors), we find a singularity in the case where 1−WzxWxz − WzyWyz = 0. If we choose weighting factors in just this way, then arbitrary data at v and w cannot be continued to a global solution. Indeed, if the scalar field is everywhere non-negative, then this particular choice of dynamics puts ironclad constraints on the value of the field at v and w: the field there must be zero (assuming Wvx and Wwy to be non-zero), and similarly all nodes in their past must have field value zero. If the field can take negative values, then the values at v and w must be so chosen that vWvxWxz = −wWwyWyz. In either case, the field values at v and w are severely constrained by the existence of the CTC region even though these nodes lie completely to the past of that region. It is this sort of constraint which we find to be unlike anything which appears in standard physics.