The QDL Mass-Occupancy Principle: Compton–de Broglie Clock Closure and Planck-Normalized Mass Structure

The dimensionless quantity Gm^2/hbar c is conventionally recognized as the gravitational self-coupling of a mass m, equivalently the squared Planck-normalized mass. It also admits familiar geometric and temporal forms, including rg/lambdaC and tg omegaC. These identities are standard. This paper does not claim their mathematical discovery. Instead, it proposes a structural reinterpretation within the Quantized Dimensional Ledger (QDL) framework: the gravitational self-coupling admits a natural factorization as a Compton-gravitational occupancy of the Quantized Dimensional Cell. In QDL, the gravitational parameter Gm realizes the distinguished dimensional cell L^3F^2, while the Compton angular frequency omegaC realizes the de Broglie internal clock associated with rest mass. Their closure product chi_m = Gm omegaC/c^3 = Gm^2/hbar c = (m/mP)^2 is interpreted as a mass-occupancy number: the degree to which a Compton-localized clock occupies its own gravitational dimensional cell. In this interpretation, the Planck mass is the saturated occupancy state chi_m = 1, elementary particles are deeply sub-saturated occupancy states, and the particle mass hierarchy can be reformulated as a hierarchy of QDC occupancy depths. The paper establishes the QDL factorization of the known invariant, relates it to de Broglie’s internal clock idea, compares the proposal with standard Planck-scale and gravitational-coupling interpretations, and develops a minimal occupancy-depth diagnostic for electroweak Yukawa projections. The diagnostic does not derive the particle mass spectrum, but it converts the Yukawa hierarchy into a finite set of electroweak occupancy projection depths that any future QDL admissibility rule must reproduce.