A deterministic algorithm for signing bipartite graphs at the Ramanujan bound

We give a deterministic polynomial-time algorithm for the Bilu–Linial signing problem on bipartite graphs. For every finite simple bipartite graph of maximum degree at most an integer $\mathrm{\Delta }\ge 3$, the algorithm assigns signs to its edges so that the signed adjacency matrix has operator norm strictly less than $2\sqrt{\mathrm{\Delta }-1}$. Our algorithm builds on the randomized recursive repair framework of Jadbabaie, Saberi, and Sra~\cite{JSS26}, with deterministic rules for sign selection and vertex deletion.