Certified branch-safe selective writing in diffusively coupled bistable graph memories

We study a finite weighted undirected graph of identical smooth two-component bistable cells with symmetric nonnegative diffusive coupling. We derive explicit sufficient conditions for storage of prescribed binary patterns, certified branch-safe switching of a single selected node by a constant pulse, and componentwise bounds on write-induced crosstalk. The switching certificate guarantees that every non-target node remains on its original branch throughout the transient and provides a computable sufficient pulse duration. The results apply uniformly over the entire certified source box and require no computation of separatrices or basins of attraction. A worked example on an irregular weighted graph illustrates the complete certification chain and its conservativeness.