Grundy Total Domination and Skew Zero Forcing in Cartesian Products of Paths and Cycles

What the math gives to ML

The paper supplies exact combinatorial observability budgets for rectangular, cylindrical, and toroidal grid graphs through skew zero forcing, together with the identity connecting these budgets to maximum skew nullity and Kronecker-difference matrix constructions. The transferable asset is not the domination parameter itself, but a way to choose a small set of anchor nodes and an explicit sequential propagation order that reaches every node under a sparse local graph pattern. This can define causal lattice mixers or sparse graph-recurrent networks whose update masks are guaranteed to cover the entire latent grid, including parity-sensitive cases on periodic boundaries. The most credible first use is a structured sparse message-passing architecture for masked-grid reconstruction or long-horizon spatial state propagation, compared against ordinary fixed-depth grid convolutions.