The Quantized Dimensional Cell in Gravitational Dynamics: GM, Keplerian Closure, and Dimensional Admissibility

This preprint presents a QDL admissibility theorem identifying the gravitational parameter μ = GM as a direct realization of the Quantized Dimensional Cell (QDC) dimensional form L³F². The result is framed as a structural interpretation of standard Keplerian dynamics, not as a modification of Newtonian gravity or a numerical derivation of G. Physical constants are often introduced as numerical values to be memorized, but in physical modeling they serve a deeper structural function: they connect otherwise distinct dimensional sectors. The Quantized Dimensional Ledger (QDL) formalism represents dimensional quantities as integer-valued ledger vectors and tests constructed expressions against declared closure targets. Within this framework, the Quantized Dimensional Cell (QDC), with dimensional form L³ F², has been proposed as a primitive closure target combining three-dimensional spatial extent with second-order dynamical frequency structure. This paper identifies a direct and elementary realization of the QDC in gravitational dynamics. The gravitational parameter μ = GM has dimensions L³ F², exactly matching the QDC form. Standard Keplerian orbital closure may be written as μ = r³ω² for circular motion, showing that a spatial scale cubed and an orbital frequency squared combine into the gravitational parameter of the source. Familiar quantities such as surface gravity, escape velocity, and gravitational potential then appear as lower-dimensional projections of this QDC-form object. The result does not claim to derive the numerical value of G, the mass M, or the measured value of μ. Rather, it shows that one of the most operationally central parameters in gravitational physics naturally realizes the QDC dimensional target. This provides a concrete physical anchor for QDL closure: the QDC is not merely an abstract dimensional form, but appears in the standard structure of orbital mechanics. The paper develops this result as a modest but foundational admissibility theorem, clarifying the distinction between dimensional homogeneity, QDL closure, and numerical prediction.