Minimal Kernel Dimension for Fixed-Control Balance-Loop Realizations of Rational Floor Maps

Paper XII. Minimal Kernel Dimension for Fixed-Control Balance-Loop Realizations of Rational Floor Maps. Preprint, August 2026. This paper introduces the minimal kernel dimension of an exact fixed-control balance-loop realization of a rational floor map. For the partial map x ↦ floor(Qx/d), defined on integers not divisible by d, the invariant κ(d,Q) measures the least relation-lattice [ ] The post…