Universal-constant conjecture for optimal balanced discrepancy

Let $k\geq 4$, and let $\delta^*(k)$ denote the optimal balanced discrepancy for the module-lattice sign-selection problem. Write $\delta^*$ for the constant value proposed by the conjecture. Universal-constant conjecture. For all $k\geq 4$, the optimal balanced discrepancy is a universal constant

$$\delta^*(k)=\delta^*\approx 0.4407,$$

independent of $k$. The value is supported computationally by certified MILP optimizations for $k\in\{4,\dots,10\}$ and independent local-search verification; its precise number-theoretic identification remains open.