The Arithmetic Lift: Rigidity and the Open Packaging Problem

Paper 50 in the open-access research programme "The Geometry of the Critical Line." This paper proves that after the sterile carrier (Paper 49) and the prime-power amplitudes (Paper 47) are fixed, the remaining arithmetic-lift problem is uniquely determined and reducible to a single operator-valued packaging problem in the Bost–Connes crossed product. The main results are: (1) A rigidity theorem showing that at most one admissible arithmetic extension exists on the sterile kernel class — once the arithmetic support, reduced identity functional, and prime-power amplitudes are frozen, the scalar target is unique. (2) A reduction theorem showing that any packaging map satisfying the operator-valued packaging…