Minimize the basic function set needed for the RCD characterization

Identify a minimal set of basic functions which, together with composition and the robust ODE schema, suffices to characterize FPSPACE as in the RCD framework; equivalently, determine the smallest generating set of base functions that preserves the established FPSPACE characterizations for both discrete and real-valued functions.

Background

The current RCD algebra employs a collection of base functions (including arithmetic operations, tanh, cos, constants such as π, and simple scalings) closed under composition and the robust ODE schema. The authors note that many of these functions can themselves be realized via ODEs and did not attempt to minimize this generating set.

Establishing a minimal or near-minimal basis would clarify which primitives are essential for the precision-based space characterization, and could streamline future theoretical developments and implementations.