Necessity of the a b constructor in the Richter operator

Ascertain whether the binary constructor a b in the Richter operator is necessary; specifically, determine if Richterian notation systems and associated coding results can be obtained without including the a b constructor.

Background

In developing Richterian ordinal notation systems, the operator includes the binary constructor written as a b. The authors remark that this component is technically motivated, but its indispensability is unclear.

Clarifying whether the a b constructor is actually needed (or whether equivalent strength and coding properties follow without it) would streamline the definition of Richterian systems and align with earlier doubts raised by Richter regarding the necessity of this constructor.