A Derivation-First Exponent Map for Planck Quantities and Gravitational Coupling

This preprint presents a derivation showing that all standard Planck quantities, together with the gravitational coupling constant, can be expressed exactly as monomials in Planck time, reduced Planck’s constant, and the speed of light with integer exponents. Beginning from the conventional Planck definitions, the Planck-time expression is rearranged to obtain an exact identity for the gravitational coupling G, which is then substituted into each remaining definition. This yields a compact generalized representation Q = tₚᵃ ℏᵇ cⁿ and a complete exponent map for the Planck quantities and gravitational coupling, without introducing additional constants or assumptions. This result exposes a previously implicit algebraic closure underlying the Planck system. Version 1.0 — derivation-first formulation with explicit integer exponent closure.