The Emergence of a Dimensionless Scale Parameter from the Planck Exponent Basis

This paper demonstrates that once the standard Planck quantities and the gravitational coupling constant are expressed in a closed monomial exponent basis, the existence of a unique dimensionless scale parameter is unavoidable. That parameter,N = M / mₚ = E / Eₚ,emerges directly from the Planck definitions without introducing new constants or assumptions. Scale is shown to enter physics solely through counting, establishing a strict separation between invariant Planck-scale structure and system-dependent realisation.The result provides a necessary structural bridge between exact Planck derivations and macroscopic physics.